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 example
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.
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: 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.
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