Two-Step Equations & Inequalities
Aligned to 7.EE.B.4 — Common Core State Standards for Mathematics.
What this lesson teaches
Undo operations in reverse order: first undo addition/subtraction, then undo multiplication/division. For inequalities, flip the sign if you multiply or divide by a negative.
Worked examples
Example 1
3x + 4 = 19 → subtract 4 → 3x = 15 → divide by 3 → x = 5. Check: 3(5)+4 = 19. ✓
Example 2
(x/4) − 2 = 6 → add 2 → x/4 = 8 → multiply by 4 → x = 32.
Example 3
Multiplying or dividing an inequality by a negative flips it: −2x < 10 becomes x > −5, not x < −5.
Practice questions
- Solve 2x − 7 = 11.
- Solve 5 − 2x = 13.
- Solve the inequality −3x > 12 and graph the solution.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Ecuaciones e Inecuaciones de Dos Pasos
Deshaz las operaciones en orden inverso: primero deshaz la suma o resta, luego deshaz la multiplicación o división. En las inecuaciones, invierte el signo si multiplicas o divides por un número negativo.
Ejemplo 1: 3x + 4 = 19 → resta 4 → 3x = 15 → divide entre 3 → x = 5. Comprueba: 3(5) + 4 = 19. ✓
Ejemplo 2: (x/4) − 2 = 6 → suma 2 → x/4 = 8 → multiplica por 4 → x = 32.
Ejemplo 3: Multiplicar o dividir una desigualdad por un negativo la voltea: −2x < 10 se vuelve x > −5, no x < −5.
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