Question

question 6 (1 point) which of the following number lines depicts the solution to 4(x + 1)>16 + 7x? the darker sections should represent the answer a) <---|-----|-----|-----|-----|-----|-----|-----|-----|----> -7 -6 -5 -4 -3 -2 -1 0 1 2 3 ℝ b) <---|-----|-----|-----|-----|-----|-----|-----|-----|----> -7 -6 -5 -4 -3 -2 -1 0 1 2 3 ℝ c) <---|-----|-----|-----|-----|-----|-----|-----|-----|----> -7 -6 -5 -4 -3 -2 -1 0 1 2 3 ℝ d) <---|-----|-----|-----|-----|-----|-----|-----|-----|----> -7 -6 -5 -4 -3 -2 -1 0 1 2 3 ℝ

Explanation:

Step1: Expand the left - hand side

$4(x + 1)=4x+4$, so the inequality becomes $4x + 4>16 + 7x$.

Step2: Move the $x$ terms to one side

Subtract $4x$ from both sides: $4x+4-4x>16 + 7x-4x$, which simplifies to $4>16 + 3x$.

Step3: Move the constant terms to one side

Subtract 16 from both sides: $4-16>16 + 3x-16$, resulting in $- 12>3x$.

Step4: Solve for $x$

Divide both sides by 3: $\frac{-12}{3}>\frac{3x}{3}$, so $x<-4$.

Answer:

The number - line that has an open circle at $-4$ and is shaded to the left of $-4$ represents the solution. Without seeing the full shading of options a, b, c, d, if we assume the standard convention of open - circle for $>$ or $<$ and shading in the appropriate direction, the correct number - line is the one with an open circle at $-4$ and shading to the left. If option c has an open circle at $-4$ and shading to the left, then the answer is c.