What It Means to Solve
Aligned to 6.EE.B.5 — Common Core State Standards for Mathematics.
What this lesson teaches
Solving an equation or inequality means finding the value (or values) of the variable that make it true. You can check any candidate by substituting it back in.
Worked examples
Example 1
Does x = 6 solve x + 4 = 10? Substitute: 6 + 4 = 10. True, so 6 is a solution. Does x = 6 satisfy x > 5? Yes, since 6 is greater than 5.
Example 2
Does x = 3 solve 2x − 1 = 7? Substitute: 2(3) − 1 = 5, not 7. So no, 3 is not a solution.
Example 3
An equation usually has one solution; an inequality has many. x > 5 is true for 5.1, 6, 100 — infinitely many numbers.
Practice questions
- Is n = 8 a solution of n − 3 = 5? Check it.
- Which of 2, 4, or 7 make x > 5 true?
- Test whether y = 9 makes 2y = 18 true.
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
Qué Significa Resolver
Resolver una ecuación o desigualdad significa hallar el valor (o los valores) de la variable que la hacen verdadera. Puedes comprobar cualquier candidato sustituyéndolo de nuevo.
Ejemplo 1: ¿x = 6 resuelve x + 4 = 10? Sustituye: 6 + 4 = 10. Es verdadero, así que 6 es solución. ¿x = 6 cumple x > 5? Sí, porque 6 es mayor que 5.
Ejemplo 2: ¿x = 3 resuelve 2x − 1 = 7? Sustituye: 2(3) − 1 = 5, no 7. Entonces no, 3 no es solución.
Ejemplo 3: Una ecuación suele tener una solución; una desigualdad tiene muchas. x > 5 es verdadero para 5.1, 6, 100 — infinitos números.
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