6.EE.B.7 6th Grade Expressions & Equations

Solving One-Step Equations

Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for non-negative rational numbers.

How to explain it

At this standard, students solve one-step equations using inverse operations.

The anchor students hold onto: Use the INVERSE OPERATION — undo what was done to the variable, applying the same step to BOTH sides of the equation.

The inverse-operation strategy extends to inequalities (6.EE.B.8) — solving x + p < q and px > q uses the same steps, but solutions become ranges on a number line rather than single values.

Worked examples

Example 1

Solve: n + 6 = 14

Step 1Operation: + 6; inverse: − 6

Step 2Subtract 6 from both sides: n = 14 − 6

Step 3n = 8

Answern = 8

Example 2

Solve: n/3 = 7

Step 1Operation: ÷ 3; inverse: × 3

Step 2Multiply both sides by 3: n = 7 × 3

Step 3n = 21

Answern = 21

Common mistakes

What students write Student solves 6n = 48 by multiplying both sides by 6, getting n = 288.

The fix To undo multiplication, DIVIDE both sides: n = 48 ÷ 6 = 8. Use the inverse operation.

Try this A student solves n + 7 = 20 and writes n = 27. Identify the error and give the correct solution.

What students write Student solves n + 8 = 15 by adding 8 to both sides (same operation, not inverse).

The fix Use the INVERSE: subtract 8 from both sides — n = 15 − 8 = 7.

Try this A student solves 6n = 48 and writes n = 288. Identify the error and give the correct solution.

Teacher tip

Head off the two predictable errors before they happen. First: To undo multiplication, DIVIDE both sides: n = 48 ÷ 6 = 8. Use the inverse operation. Second: Use the INVERSE: subtract 8 from both sides — n = 15 − 8 = 7.