Question

name
period
date
equations summative
math rti - dover high school

1. select all of the equations that can model the relationship shown in the tape diagram:

a. $2x + 7 = 25$
b. $25 = x + 2 + 7$
c. $2x = 25 - 7$
d. $25 - 2x = 7$
e. $x^2 + 7 = 25$
(tape diagram: three parts labeled x, x, 7; total labeled 25)

Explanation:

The tape diagram shows two parts of \( x \), one part of \( 7 \), and the total is \( 25 \). So the sum of \( 2x \) and \( 7 \) is \( 25 \), which gives the equation \( 2x + 7 = 25 \) (option a). We can also rearrange this equation:

Step 1: Rearrange to solve for \( 2x \)

Subtract \( 7 \) from both sides of \( 2x + 7 = 25 \), we get \( 2x = 25 - 7 \) (option c).

Step 2: Rearrange to solve for \( 25 - 2x \)

Subtract \( 2x \) from both sides of \( 2x + 7 = 25 \), we get \( 25 - 2x = 7 \) (option d).

Now check the other options:

• Option b: \( 25 = x + 2 + 7 \) simplifies to \( 25 = x + 9 \), which is not equivalent to the tape diagram's relationship.
• Option e: \( x^2 + 7 = 25 \) involves \( x^2 \), but the tape diagram has two \( x \) terms (linear, not quadratic), so this is incorrect.

Answer:

a. \( 2x + 7 = 25 \), c. \( 2x = 25 - 7 \), d. \( 25 - 2x = 7 \)