Question

solve word problems by solving inequalities
question id : 603673

which number line represents the solution to the inequality
$-4w + 7 < 75$ ?

a
<---|-20 -16 -12 -8 -4 0 4 8 12 16 20--->
b
<---|-20 -16 -12 -8 -4 0 4 8 12 16 20--->
c
<---|-20 -16 -12 -8 -4 0 4 8 12 16 20--->
d
<---|-20 -16 -12 -8 -4 0 4 8 12 16 20--->

Explanation:

Step1: Solve the inequality for \(w\)

Subtract \(7\) from both sides:
\(-4w+7 - 7<75 - 7\)
\(-4w<68\)
Divide both sides by \(-4\) and reverse the inequality sign (since dividing by a negative number):
\(w > - 17\)

Step2: Analyze the number - line representation

A number - line with an open circle at \(-17\) (because the inequality is strict, \(w
eq - 17\)) and an arrow pointing to the right (since \(w\) is greater than \(-17\))

Answer:

Assuming the number - line in option B has an open circle at \(-17\) and an arrow to the right (as per the solution \(w > - 17\)), the answer is B.