Question

solve the inequality. graph the solution set and write it in interval notat
2(2x + 1) < 2
choose the correct graph below.
a.
< -10 -8 -6 -4 -2 0 2 4 6 8 10
b.
c.
< -10 -8 -6 -4 -2 0 2 4 6 8 10
d.
write the answer in interval notation.
(type your answer in interval notation.)

Explanation:

Step1: Expand the left - hand side

$2(2x + 1)=4x+2$, so the inequality becomes $4x + 2<2$.

Step2: Subtract 2 from both sides

$4x+2 - 2<2 - 2$, which simplifies to $4x<0$.

Step3: Divide both sides by 4

$\frac{4x}{4}<\frac{0}{4}$, resulting in $x < 0$.

To graph the solution set, we draw a number line. We put an open circle at 0 (since $x$ is strictly less than 0, not equal to 0) and shade the line to the left of 0.

In interval notation, the solution set is $(-\infty,0)$.

Answer:

The correct graph is the one with an open - circle at 0 and shading to the left. In interval notation: $(-\infty,0)$