Question

unit ii hw#4
name
per
reflect
write your response in the box.
emily solved the inequality as shown below. which describes the error that emily made in her work?
-2.5x + 5 < 10
-2.5x < 15
x > -6
a. emily did not combine 5 and 10 correctly.
b. emily did not flip the inequality sign.
c. emily did not divide correctly.
d. emily did not make an error in her work.
i’m still confused about...
practice
for problems 13 - 16, solve and graph the equation and inequalities.

1. -5(x + 7) > 25
2. 3(x - 10) < 18
3. -4(x - 5) = 36
4. -6(x + 8) ≤ 30

Explanation:

First Problem (Emily's Inequality Error)

Step1: Check constant subtraction

Subtract 5 from both sides:
$-2.5x + 5 - 5 < 10 - 5$
$\implies -2.5x < 5$

Step2: Analyze Emily's mistake

Emily got $-2.5x < 15$, which is wrong. She incorrectly calculated $10-5$ as 15 instead of 5.

Problem 13: Solve $-5(x + 7) > 25$

Step1: Divide by -5, flip sign

$\frac{-5(x+7)}{-5} < \frac{25}{-5}$
$\implies x + 7 < -5$

Step2: Subtract 7 from both sides

$x + 7 - 7 < -5 - 7$
$\implies x < -12$

Problem 14: Solve $3(x - 10) < 18$

Step1: Divide both sides by 3

$\frac{3(x-10)}{3} < \frac{18}{3}$
$\implies x - 10 < 6$

Step2: Add 10 to both sides

$x - 10 + 10 < 6 + 10$
$\implies x < 16$

Problem 15: Solve $-4(x - 5) = 36$

Step1: Divide both sides by -4

$\frac{-4(x-5)}{-4} = \frac{36}{-4}$
$\implies x - 5 = -9$

Step2: Add 5 to both sides

$x - 5 + 5 = -9 + 5$
$\implies x = -4$

Problem 16: Solve $-6(x + 8) \leq 30$

Step1: Divide by -6, flip sign

$\frac{-6(x+8)}{-6} \geq \frac{30}{-6}$
$\implies x + 8 \geq -5$

Step2: Subtract 8 from both sides

$x + 8 - 8 \geq -5 - 8$
$\implies x \geq -13$

Answer:

A. Emily did not combine 5 and 10 correctly.

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Practice Problems 13-16