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6-8 Grado 7 Unit 6 Lesson 8

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Unit 6, Lesson 8

Razonemos sobre la resolución de ecuaciones (parte 2)

Grado 7

Practice

Problem 1

Este es el diagrama de un colgador balanceado:

Escribe una ecuación que represente el diagrama.
Resuelve la ecuación razonando sobre el colgador o sobre la ecuación. Explica tu razonamiento.

Hanger has 5 groups of a circle + rectangle labeled with 2 on the left, rectangle labeled with 11 on the right

Problem 2

Explica cómo cada parte de la ecuación \(9=3(x+2)\) se representa en el diagrama de colgador.

\(x\)
9
3
\(x+2\)
\(3(x+2)\)
el signo igual

Balanced hanger, left side, 9 squares each labeled 1. Right side, three groups, each group contains one circle labled x and 2 squares labeled 1.

Problem 3

ForLesson 11: Contextos de porcentajes

De la siguiente lista, selecciona la palabra que describe mejor cada situación.

Depositas dinero en una cuenta de ahorros, y cada año la cantidad de dinero en la cuenta aumenta en un 2.5%.
Por cada automóvil que vende, a un vendedor se le paga un 6% del precio del automóvil.
Un cliente de un restaurante paga un 20% extra del precio de la comida. Este dinero extra es para la persona que sirvió la comida.
Una tienda de muebles antiguos paga \$200 por una silla, le suma un 50% de esa cantidad y la vende por \$300.
El precio normal de un colchón es $600, pero está en oferta y cuesta un 10% menos.
Por cada artículo que compres en Texas, pagas un 6.25% adicional del precio del artículo al gobierno estatal.

Problem 4

ForLesson 3: Razonemos sobre ecuaciones usando diagramas de cinta

Clare dibujó este diagrama para la ecuación \(2x+16=50\), pero cuando usó este diagrama obtuvo una solución incorrecta.

A tape diagram partitioned into three different sized rectangles, labeled 2, x and 16. The total length of the bar is labeled 50.

¿Qué valor de \(x\) se puede encontrar al usar el diagrama?
Muestra cómo arreglar el diagrama de Clare para que este corresponda con la ecuación de forma correcta.
Usa el nuevo diagrama para encontrar el valor correcto de \(x\).
Explica cuál fue el error de Clare cuando dibujó su diagrama.

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