Undo in reverse order. 3x + 5 = 20: subtract 5 to get 3x = 15, then divide by 3 to get x = 5. A tape diagram helps with a story: a $135 bill is $45 plus some $30 hours. Take off $45, and $90 is x pieces of $30, so x = 3.
Worked example
Solve 3x + 6 = 18. x = ?
Answer:4
Undo the + 6 first: subtract 6 from both sides. 3x = 18 − 6 = 12. Now undo the multiplying: divide both sides by 3. x = 12 ÷ 3 = 4. Check: 34 + 6 = 18.
For grown-ups: Linear expressions with rational coefficients; two-step equations (px + q = r) and inequalities. Below: three problems to try with the worked answers, and a free printable sheet. Children can practise the same skill as a game, with no sign-up and no ads.
CCSS 7.EE.A
What this practises, for teachers
Practices linear expressions with rational coefficients; two-step equations (px + q = r) and inequalities (7.EE.A). A printable sheet with its answer key, worked answers on the page, no accounts.
Undo the + 2 first: subtract 2 from both sides. 2x = 12 − 2 = 10. Now undo the multiplying: divide both sides by 2. x = 10 ÷ 2 = 5. Check: 25 + 2 = 12.
Solve 4x + 6 = 30. x = ?
Show the answer and how
Answer:6
Undo the + 6 first: subtract 6 from both sides. 4x = 30 − 6 = 24. Now undo the multiplying: divide both sides by 4. x = 24 ÷ 4 = 6. Check: 46 + 6 = 30.
A student owes $31 and pays back $4 every week. After how many weeks will $7 still be owed?
Show the answer and how
Answer:6 weeks
Let x be the answer. The story gives the equation −4x + 31 = 7. Picture a tape diagram: the whole tape is 7, the fixed starting amount 31 is one piece, and the rest is taken away in x equal pieces. Undo the + 31 first: subtract 31 from both sides. −4x = 7 − 31 = −24. Now undo the multiplying: divide both sides by −4. x = −24 ÷ (−4) = 6. Check: −46 + 31 = 7.