Question

solve the inequality and graph the solution. -2(d - 4) ≤ 6 plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

Explanation:

Step1: Distribute -2

$-2(d - 4)=-2d+8$, so the inequality becomes $-2d + 8\leq6$.

Step2: Subtract 8 from both sides

$-2d+8 - 8\leq6 - 8$, which simplifies to $-2d\leq - 2$.

Step3: Divide both sides by -2 and reverse the inequality sign

Since we are dividing by a negative number, the inequality sign flips. So $\frac{-2d}{-2}\geq\frac{-2}{-2}$, resulting in $d\geq1$.

Answer:

The solution of the inequality is $d\geq1$. On the number - line, we plot a closed - circle at $d = 1$ (because the inequality includes equality, $\geq$) and draw a ray to the right of $1$ towards positive infinity.