Solving Linear Equations
Aligned to 8.EE.C.7 — Common Core State Standards for Mathematics.
What this lesson teaches
Solve by using the distributive property, combining like terms, and getting the variable on one side. If the equation simplifies to a true statement like 5 = 5, there are infinitely many solutions; if it gives a false one like 3 = 7, there is no solution.
Worked examples
Example 1
Solve 3(x + 2) = 2x + 11. Distribute: 3x + 6 = 2x + 11. Subtract 2x: x + 6 = 11. Subtract 6: x = 5. This equation has one solution.
Example 2
Solve 4x + 3 = 4x + 3. Both sides are identical, so every number works — infinitely many solutions.
Example 3
Solve 2x + 5 = 2x + 9. Subtracting 2x gives 5 = 9, which is false, so there is no solution at all.
Practice questions
- Solve 4x − 7 = 2x + 9.
- Solve 2(x + 3) = 2x + 6 and describe the number of solutions.
- Solve 5x + 1 = 5x − 4 and describe the number of solutions.
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 Lineales
Resuelve usando la propiedad distributiva, combinando términos semejantes y dejando la variable de un solo lado. Si la ecuación se reduce a una afirmación verdadera como 5 = 5, hay infinitas soluciones; si da una falsa como 3 = 7, no hay solución.
Ejemplo 1: Resuelve 3(x + 2) = 2x + 11. Distribuye: 3x + 6 = 2x + 11. Resta 2x: x + 6 = 11. Resta 6: x = 5. Esta ecuación tiene una solución.
Ejemplo 2: Resuelve 4x + 3 = 4x + 3. Los dos lados son idénticos, así que cualquier número sirve — infinitas soluciones.
Ejemplo 3: Resuelve 2x + 5 = 2x + 9. Restar 2x da 5 = 9, que es falso, así que no hay ninguna solución.
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