Solve an equation by keeping both sides equal. Start with one-step equations using nonnegative values, or choose two-step equations with signed numbers.
Use the working space to record the inverse operation on both sides. Then substitute the solution into the original equation rather than relying only on the answer key.
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In x + 7 = 19, subtract 7 from both sides to find x = 12. Substitution checks it: 12 + 7 = 19. For 3x = 18, divide both sides by 3 to get x = 6.
For 3x + 5 = 20, subtract 5 from both sides to get 3x = 15. Divide both sides by 3 to find x = 5. The check is 3 × 5 + 5 = 20.
The two-step extension can give values that are not positive whole numbers. For example, 2x − 3 = −10 becomes 2x = −7, so x = −7/2 = −3.5. This still gives a valid equality when substituted.
Nonnegative one-step equation work is a sixth-grade starting point. Two-step equations with signed values are a seventh-grade extension. An equals sign states a relationship between two expressions; it is not simply an instruction to calculate whatever comes next.