Practice Solving Algebra Equations – with Video Solutions
- Posted by Brian Stocker MA
- Date October 11, 2012
- Comments 36 comments
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Algebra Practice Questions
1. 5x + 3 = 7x – 1. Find x
a. 1/3
b. ½
c. 1
d. 2
2. 5x + 2(x + 7) = 14x – 7. Find x
a. 1
b. 2
c. 3
d. 4
3. 12t – 10 = 14t + 2. Find t
a. -6
b. -4
c. 4
d. 6
4. 5(z + 1) = 3(z + 2) + 11 Solve for Z
a. 2
b. 4
c. 6
d. 12
5. The price of a book went up from $20 to $25. By how many percent did the price increase?
a. 5
b. 10
c. 20
d. 25
6. The price of a book decreased from $25 to $20. By how many percent did the price decrease?
a. 5
b. 10
c. 20
d. 25
7. After taking several practice tests, Brian improved the results of his GRE test by 30%. Given that the first time he took the test Brian had answered 150 questions correctly, how many correct answers did he answer in the second test?
a. 105
b. 120
c. 180
d. 195
8. A number is increased by 2 and then multiplied by 3. The result is 24. What is this number?
a. 4
b. 6
c. 8
d. 10
9. My father’s age divided by 5 is equal to my brother’s age divided by 3. My brother is 3 years older than me. My father’s age is 3 less than 2 times my age. How old is my father?
a. 34
b. 45
c. 56
d. 61
10. (x – 2) / 4 – (3x + 5) / 7 = – 3, x = ?
a. 6
b. 7
c. 10
d. 13
11. 1 / (1 + 1 / (1 – 1/x)) = 4, x = ?
a. – 3/4
b. 3/7
c. 4/7
d. 3/4
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Algebra Problem Answer Key
Common Mistakes Answering Linear Equation Questions
- Misinterpreting the Question or Setting Up the Equation Incorrectly
- Failing to properly understand what the question is asking.
- Confusing linear equations with other types of algebra.
- Misreading the problem and setting up the wrong equation.
- Basic Arithmetic Errors
- Addition, subtraction, multiplication, or division errors. Basic Math Practice
- Incorrectly applying the order of operations (PEMDAS). Order of Operation Practice
- Solving for the Wrong Variable:
- Solving for the wrong variable.
- Sign Errors:
- Incorrectly using positive and negative signs.
- Failing to change the sign when performing basic operations.
- Fractions and Decimals:
- Incorrectly converting between fractions, decimals, and percentages. Factions, decimals and percent practice
- Incorrect Distribution
- Mistakes when applying the distributive property.
- Forgetting to distribute a negative sign through parentheses.
- Incorrectly Combining Like Terms
- Failing to properly combine like terms.
- Mistaking terms that are not alike for like terms.
- Skipping Steps:
- Skipping steps in the process, leading to errors in the solution.
- Not showing work, making it hard to identify where a mistake was made.
- Checking Solutions:
- Forgetting to plug the solution back into the original equation to check its correctness.
- Assuming an answer is correct without verification.
- Mistakes Graphing
- Errors plotting or connecting points.
- Misinterpreting the slope and intercept in the line equation.
- Time Management:
- Spending too much time on one problem and rushing through others.
- Not allocating enough time to review and check answers. Time Management on a Test
- Anxiety and Pressure:
- Feeling overwhelmed or stressed causing incorrect answers.
- Making careless mistakes due to test anxiety. Test Anxiety Tips
1. D
5x + 3 = 7x – 1
first we need to collect like terms
second is to undo addition and subtraction
third and the last is to undo multiplication and division
so again the first step is to put 5x and 7x in one side = 7x-5x
second put 3 and 1 in one side = 7x – 5x = 3 + 1
now we will solve the answer = 2x = 4
now we will divide by 2 to the both sides
2x/2 = 4/2
the answer now is x=2
1. Video Solution
2. C
5x + 2(x + 7) = 14x – 7
5x + 2x + 14 = 14x – 7
7x + 14 = 14x – 7
7x – 14x = -14 – 7
-7x = -21
x = 3
2. Video Solution
3. A
12t – 10 = 14t + 2
12t – 14t = 10 + 2
-2t = 12
-t = 6
t = -6
3. Video Solution
4. C
5(z + 1) = 3(z + 2) + 11. Z=?
5z + 5 = 3z + 6 + 11
5z + 5 = 3z + 17
5z = 3Z + 17 – 5
5z – 3z = 12
2z = 12
z = 6
4. Video Solution
Answer Key
5. D
The price increased from $20 to $25 ($5) so the question is 5 is what percent of 20. Or, 5/20 = x/100 ; 500/20 = 25%
6. C
7. D
The first time, Brian answered 150 questions correctly and the second time he answered 30% more correctly, so,
150 + (30/100 * 150) ; 30% of 150 = 45, or (30 * 150)/100
so 150 + 45 = 195
8. B
Let us call this number by x:
This number is increased by 2: x + 2
Then, it is multiplied by 3: 3(x + 2)
The result is 24: 3(x + 2) = 24 … Solving this linear equation, we obtain the value of the number:
3(x + 2)/3 = 24 /3 Divide both sides by 3 and cancel out
x + 2 = 24 / 3
x + 2 = 8
x = 8 – 2 – 2 crosses the equal sign so negative
x = 6
9. B
My age: x
My brother is 3 years older than me: x + 3
My father is 3 less than 2 times my age: 2x – 3
My father’s age divided by 5 is equal to my brother’s age divided by 3: (2x – 3) / 5 = (x + 3) / 3
By cross multiplication:
5(x + 3) = 3(2x – 3)
5x + 15 = 6x – 9
x = 24
My father’s age: 2.24 – 3= 48 – 3 = 45
10. C
There are two fractions containing x and the denominators are different. First, let us find a common denominator to simplify the expression. The least common multiplier of 4 and 7 is 28. Then,
7(x – 2) / 28 – 4(3x + 5) / 28 = – 3.28 / 28 … Since both sides are written on the denominator 28 now, we can eliminate them:
7(x – 2) – 4(3x + 5) = – 84
7x – 14 – 12x – 20 = – 84
– 5x = – 84 + 14 + 20
– 5x = – 50
x = 50/5
x = 10
11. B
We can follow outside to inside method to solve this type of problems. x is in the inner part of this fraction; then, we need to narrow the circle to reach x:
1 / (1 + 1 / (1 – 1/x)) = 4
This means that (1 + 1 / (1 – 1/x)) is equal to 1/4. Then,
1 + 1 / (1 – 1/x) = 1/4
1 / (1 – 1/x) = 1/4 – 1
1 / (1 – 1/x) = – 3/4
This means that 1 – 1/x = – 4/3. Then,
1 – 1/x = – 4/3
1 + 4/3 = 1/x
1/x = 7/3
So, x = 3/7.
Most Common Algebra Questions on a Test
- Simplifying algebraic expressions using the order of operations (PEMDAS)
- Solving linear equations
- Factoring polynomials
- Graphing linear equations and understanding the slope and y-intercept
- Solving systems of linear equations
- Simplifying radicals and working with rational exponents
- Quadratic equations and completing the square
- Exponents and exponential functions
- Logarithms and their properties
- The binomial theorem and binomial expansion
Most Common Algebra Mistakes on a Test
- Incorrectly using order of operations (PEMDAS)
- Misunderstanding equations and expression
- Errors simplifying or solving expressions and equations
- Incorrectly applying algebraic properties and rules, for example distributive property, combining like terms, etc.
- Errors with polynomial operations
- Errors graphing linear equations
- Logarithms and exponential function errors
Try a FREE Algebra Quiz
Date Published: Thursday, October 11th, 2012
Date Modified: Tuesday, June 4th, 2024
Tag:Algebra
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36 Comments
I need to know how to do the formula in order to pass algebra to get accepted into a practical nursing program. Also, I need to learn basic mathematics.
you can search the formulas for basic allgebra online
In order to solve it you have to look at the two sides separated by the equal sign then combine like terms after you add or subtract from both sides so a variable(s) is on one side and the numbers are on one side then if they have a common factor divide them by the smallest of the two then you will get your answer.
Hello Will you please show me how you break this problem down in order to solve it. I read what you wrote and it makes sense but i’m visual and need to see it broken down as well as explained.
1. 5x + 3 = 7x – 1. Find x
is it 8x = 6x
4x divided by 3x x = .3333 or 1/3
haha! help. thanks.
a. 1/3
b. ½
c. 1
d. 2
5x+3=7x-1
subtract the 5x from 7x to move it to the other side to make equation 3=2x-1
now add the 1 to the 3 to move it to the other side to make the equation 4=2x
now subtract the 2 from the x to isolate the x and make the equation 4/2=x
4/2=2
X=2
No, You cannot add and subtract number just because they are next to each other. You must align same groups with each other.
5x needs ti be joined with 7x, +3 needs to be joined with -1.
However, when we align and group them, it means switching them from theyre placements where they will cross the equal sign.
The rule is, anything that has to cross the equal sign in order to group numbers will automatically have their plus and minus signs changed.
Therefore, this is how itll look.
5x + 3 = 7x – 1. Find X,
5x – 7x = – 1- 3
-2x = + 4
x = +4 / +2
x = +6
Note: 5x – 7x became -2x, as 7 is the bigger number out of the two that are being subtracted, therefore the result will adopt the minus sign from the bigger number.
Note: -1 -3 became +4 because whenever you put minus and minus together, they become a positive. Those are the rules of Algebra,
Sorry Abigale Kirsten, but that isn’t correct, -1-3 isn’t equal to +4, because that only happens in multiplication, what will happen here is it will equal -4 because -1-1 is equal to -2, if anyone disagrees please check it via a calculator.
Coming to the question, 5x + 3 = 7x – 1. Find X
We take -1 to the other side making it positive
5x+3+1=7x
This equals to
5x+4=7x
Here we now take 5x to the other side
4=7x-5x
which equals to
4=2x
we divide both sides by 2
And the answer is
x=2
I anyone doubts this please use google or a specialized calculator to check it.
thanks for the great explanation – better than mine!
Im in 7th grade and I finished this problem in 20 sec and the answer is x = 2. step by step is 5x+3=7x-1 —> you minus 5x on both sides because it is the smaller variable and you get 3 = 2x-1. The opposite of subtraction is addition, we need to isolate the x variable by getting rid of the -1 so we do (-1) + 1 is 0 and we do it on both sides of the equal sign. then the equation would be 3 + 1 = 2x -1 +1. After that, the equation would look like this: 4 = 2x then we divide the variable on both sides so it would be 4/2 = 2/2, —> then 2=x
5x + 3 = 7x – 1
1st step: minus 5x from both sides
3 = 2x + 1
2nd step: add 1 to both sides
4 = 2x
3rd step: divide both sides by 2
2 = x
Wow this is good plus who can solve this
7(x+4)-2[x-3(5+x)]=2/3(x-6)
a. 6
b.7
c.-6
d.3
is it c
Awooden block has a volume of 90cubic centimetre.find the volume of the block formed by enlarging the block with a linear scale factor of 4.
Could you explain 4 like you did 1?
OK updated solution for #4 – will get to the others soon!
Thanks Brain, really like that you explained the questions. Really help me.
for question 2. I keep getting 2 for an answer. Can you please show the breakdown on the solution.
ok!
Please no I need explanation for no 7
150 × .30 = 45 + 150 = 195
Or to make it easier, multiple by 1.30 instead of .30
Answer for question 5 should be c. 20%
The price increased from $20 to $25 ($5) so the question is 5 is what percent of 20. Or, 5/20 = x/100 ; 500/20 = 25%
THIS IS TOOOOOOO HARD IM NEVER DOING ALGEBRA AGAIN BUT I DID GET THE CORRECT ANSWER THO
or x/150=1.3 because a 30% increase is really 130% or 1.3 so if you start with x/150=1.3 you solve for x by multiplying 150 and 1.3 so the equations becomes 150*1.3=x so solving for x X=195
lol fr I am done high school and some of it is hard for me…. 🙁
can you please show me how to breakdown and solve number 11?
Can u do other questions around square and cubing digits and dividing and multiplying using algebraic equations
There are a number of 7L tins of paint and 5L tins of paint. How many tins of each do we need to make up 102L of paint?
How is this worked out in an algebra equation?
Love the questions, I just wanted to know why question 11 is 3/7 and not -1/7? Every time I plug 3/7 back into the equation I don’t get 4. Please explain this to me. Thank you
#8 can you verify this should be 18?
x+2×3=24
x+6=24
x=18
Hi – no the solution is correct – you have missed the brackets – it is 3(x + 2) which is different to x + 2 X 3 – I have added some additional steps and explanations to the answer key.
marc has 3 times more mass than his sister. His sister has a mass of 16 kg. what is marc’s mass?
derive an equation towards the statement
let marc’s mass be x
sister is 16kgs
we’re told marc is 3 times more than sister in terms of mass
therefore;
marc = xkgs=3(16)
hence x=3×16 :=48kgs
i do not understand no.5 🙁 why does it say “5 is what percent of 20” i don’t get it 🙁
Ok – the original price was $20 and it increased by $5 to the new price – $25
Original Price – $20
Increase in Price – $5
New Price – $25
To find the % increase in price –
The question becomes – Increase in Price ($5) is what percent of the Original Price ($20)
So, 5 is what percent of 20.
Or, 5/20 = x/100 ; Convert to Percent
(5/20) * 100 = (x/100) * 100 Multiply both sides of the equation by 100 to simplify
500/20 = 100/100
500/20 = 1
500/20 = 25%
Do NOT take the % of the New Price! The question asks how much did the price increase, so use the Original Price!