Question

question 7
solve the inequality and graph its solution: $-5 + 7(-8 + 4x) < -3x - 30$

a) number line with open circle at 1, red to the left

b) number line with closed circle at 1, red to the left

c) number line with open circle at 1, red to the right

d) number line with closed circle at 1, red to the right

options: a, b, c, d

Explanation:

Step1: Expand the left side

$-5 + 7(-8 + 4x) = -5 - 56 + 28x = 28x - 61$

Step2: Rewrite the inequality

$28x - 61 < -3x - 30$

Step3: Isolate x terms

$28x + 3x < -30 + 61$
$31x < 31$

Step4: Solve for x

$x < \frac{31}{31}$
$x < 1$

Step5: Match to number line

An open circle at 1, shading left.

Answer:

a) $\overleftarrow{
ule{10em}{0.2ex}} \circ_{1} \overrightarrow{
ule{8em}{0.2ex}}$ (Option a)