Question

solve the linear inequality. other than ∅, use interval notation to express the solution set and graph the solution set on a number line. -2(3x + 7) < -8x - 2 (6, ∞) (-∞, 6 (-∞, 8

Explanation:

Step1: Expand the left - hand side

$-2(3x + 7)=-6x-14$, so the inequality becomes $-6x - 14<-8x - 2$.

Step2: Add $8x$ to both sides

$-6x+8x - 14<-8x+8x - 2$, which simplifies to $2x - 14<-2$.

Step3: Add 14 to both sides

$2x-14 + 14<-2 + 14$, resulting in $2x<12$.

Step4: Divide both sides by 2

$\frac{2x}{2}<\frac{12}{2}$, so $x < 6$.

Answer:

$(-\infty,6)$
The number - line graph would have an open circle at 6 (since 6 is not included in the solution set) and an arrow pointing to the left.