Pre-Algebra Practice Questions: Solving Simple Algebraic Equations

By Mark Zegarelli

When dealing with simple algebraic expressions, you don’t always need algebra to solve them. The following practice questions ask you to use three different methods: inspecting, rewriting the problem, and guessing and checking.

Practice questions

In the following questions, solve for x in each case just by looking at the equation.

1. 18 – x = 12

2. 4x = 44

In the following questions, use the correct inverse operation to rewrite and solve each problem.

3. 100 – x = 58

4. 238/x = 17

In the following questions, find the value of x in each equation by guessing and checking.

5. 12x – 17 = 151

6. 19x – 8 = 600

Answers and explanations

  1. x = 6

    You can solve this problem through simple inspection. Because 18 – 6 = 12, x = 6.

  2. x = 11

    Again, through simple inspection, because 4(11) = 44, you know that x = 11.

  3. x = 42

    Turn the problem around by changing the subtraction to addition: 100 – x = 58 means the same thing as 100 – 58 = x, so x = 42.

  4. x = 14

    Turn the problem around by switching around the division:

    PREALGEBRA_3001

    so x = 14.

  5. x = 14

    Guess what you think the answer may be. For example, perhaps it’s x = 10:

    12(10) – 17 = 120 – 17 = 103

    103 is less than 151, so this guess is too low. Try x = 20:

    12(20) – 17 = 240 – 17 = 223

    223 is greater than 151, so this guess is too high. Therefore, x is between 10 and 20. Try x = 15:

    12(15) – 17 = 180 – 17 = 163

    163 is a little greater than 151, so this guess is a little too high. Try x = 14:

    12(14) – 17 = 168 – 17 = 151

    151 is correct, so x = 14.

  6. x = 32

    Again, start by guessing. First, try x = 10:

    19(10) – 8 = 190 – 8 = 182

    182 is much less than 600, so this guess is much too low. Try x = 30:

    19(30) – 8 = 570 – 8 = 562

    562 is still less than 600, so this guess is still too low. Try x = 35:

    19(35) – 8 = 665 – 8 = 657

    657 is greater than 600, so this guess is too high. Therefore, x is between 30 and 35. Try x = 32:

    19(32) – 8 = 608 – 8 = 600

    600 is correct, so x = 32.