# Practice Solving Algebra Equations – with Video Solutions

- Posted by Brian Stocker MA
- Date October 11, 2012
- Comments 25 comments

### Algebra on Standardized Tests

Basic Algebra is a common subject for the following exams:

See our tutorial on solving linear equations with 1 variable

### More information and Algebra Tutorials

### Try a FREE Interactive Quiz

### 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

### Try a FREE Interactive Quiz

## Algebra Problem Answer Key

### 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:

x + 2 = 24 / 3

x + 2 = 8

x = 8 – 2

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.

**Written by**, Brian Stocker MA., Complete Test Preparation Inc.

**Date Published:**Thursday, October 11th, 2012

**Date Modified:**Thursday, February 25th, 2021

Tag:Algebra

## 25 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

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

Could you explain 4 like you did 1?

OK updated solution for #4 – will get to the others soon!

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

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?