Solving Linear Equations and Inequalities
Aligned to A-REI.B.3 — Common Core State Standards for Mathematics.
What this lesson teaches
Isolate the variable by undoing operations in reverse, keeping the equation balanced. For inequalities, flip the sign when multiplying or dividing by a negative.
Worked examples
Example 1
2x − 5 = 11 → add 5 → 2x = 16 → divide by 2 → x = 8. Check: 2(8)−5 = 11. ✓
Example 2
−3x + 7 > 1 → subtract 7 → −3x > −6 → divide by −3 AND flip → x < 2.
Example 3
Check by substituting, not by re-solving. Re-doing the same steps repeats the same mistake.
Practice questions
- Solve 4x + 3 = 23.
- Solve 7 − 2x = 1.
- Solve −3x ≥ 9 and describe the solution set.
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
Resolución de Ecuaciones e Inecuaciones Lineales
Despeja la variable deshaciendo las operaciones en orden inverso, manteniendo la ecuación equilibrada. En las inecuaciones, invierte el signo cuando multiplicas o divides por un número negativo.
Ejemplo 1: 2x − 5 = 11 → suma 5 → 2x = 16 → divide entre 2 → x = 8. Comprueba: 2(8)−5 = 11. ✓
Ejemplo 2: −3x + 7 > 1 → resta 7 → −3x > −6 → divide entre −3 Y voltea → x < 2.
Ejemplo 3: Comprueba sustituyendo, no volviendo a resolver. Repetir los mismos pasos repite el mismo error.
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