Algebra Practice Questions – Solving Equations and Word Problems

Algebra on Standardized Tests

Basic Algebra is a common subject for the following exams:

College EntranceHigh School 

Nursing Entrance

See our tutorial on solving linear equations with 1 variable

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

Answer Key

1. D
5x + 3 = 7x – 1
now collect like terms
3 + 1 = 7x – 5x
every time you move something it changes signs
4 = 2x anything multiplied is divided on the other side and vice versa
4/2 = x
2 = x

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

3. A

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

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

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    16 Comments

  1. Timothy Crouse
    January 21, 2014
    Reply

    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.

    • September 7, 2015
      Reply

      you can search the formulas for basic allgebra online

    • Helpful Person
      February 4, 2017
      Reply

      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.

      • alana
        August 6, 2019
        Reply

        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

        • cal
          October 27, 2019
          Reply

          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

        • Abigale kirsten
          October 27, 2019
          Reply

          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,

  2. Sandra
    January 24, 2017
    Reply

    Could you explain 4 like you did 1?

    • Brian
      January 24, 2017
      Reply

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

  3. Tammy kent
    March 23, 2017
    Reply

    for question 2. I keep getting 2 for an answer. Can you please show the breakdown on the solution.

    • Brian
      March 23, 2017
      Reply

      ok!

  4. Odey Grace
    June 1, 2017
    Reply

    Please no I need explanation for no 7

    • Sunny
      June 4, 2018
      Reply

      150 × .30 = 45 + 150 = 195

  5. Tahmina Hossain
    February 8, 2018
    Reply

    Answer for question 5 should be c. 20%

    • Brian
      February 9, 2018
      Reply

      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. leilei
    March 7, 2019
    Reply

    THIS IS TOOOOOOO HARD IM NEVER DOING ALGEBRA AGAIN BUT I DID GET THE CORRECT ANSWER THO

    • chris
      June 29, 2019
      Reply

      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

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