# 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. 4 x = 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. 12 x – 17 = 151**

**6. 19 x – 8 = 600**

## Answers and explanations

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

*x*= 6.*x*= 11Again, through simple inspection, because 4(11) = 44, you know that

*x*= 11.*x*= 42Turn the problem around by changing the subtraction to addition: 100 –

*x =*58 means the same thing as 100 – 58 =*x*, so*x =*42.*x*= 14Turn the problem around by switching around the division:

so

*x*= 14.*x*= 14Guess 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.*x*= 32Again, 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.