Question

solve the inequality. express your answer using set notation and interval notation. graph the solution set.

-2(x + 4) < 4

the solution is expressed in set notation

the solution is expressed in interval notation as

choose the correct graph of the solution set below

a. b.

c. d.

Explanation:

Step1: Expand the left - hand side

Use the distributive property \(a(b + c)=ab+ac\). Here \(a=-2\), \(b = x\), \(c = 4\).
\(-2(x + 4)=-2x-8\). So the inequality becomes \(-2x-8\lt4\).

Step2: Add 8 to both sides

To isolate the term with \(x\), add 8 to both sides of the inequality.
\(-2x-8 + 8\lt4 + 8\), which simplifies to \(-2x\lt12\).

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

When dividing an inequality by a negative number, the direction of the inequality sign changes.
\(\frac{-2x}{-2}\gt\frac{12}{-2}\), so \(x\gt - 6\).

Answer:

• Set notation: \(\{x|x\gt - 6\}\)
• Interval notation: \((-6,\infty)\)
• Graph: Option C (assuming in option C, there is an open circle at \(x = - 6\) and the line extends to the right towards positive infinity)