 Pre-Algebra Practice Questions: Solving Simple Algebraic Equations - dummies

# Pre-Algebra Practice Questions: Solving Simple Algebraic Equations

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

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: 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.