Question

solve the inequality. express your answer using set notation and interval notation. graph the solution set. -2(x + 4) < 6 the solution is expressed in set notation as {x | □}. the solution is expressed in interval notation as □. choose the correct graph of the solution set below. options a, b, c, d with number lines.

Explanation:

Step1: Solve the inequality

Start with \(-2(x + 4) < 6\). Divide both sides by \(-2\), remembering to reverse the inequality sign: \(x + 4 > -3\). Then subtract 4 from both sides: \(x > -7\).

Step2: Set notation

In set notation, this is \(\{x | x > -7\}\).

Step3: Interval notation

For interval notation, since \(x\) is greater than \(-7\), it's \((-7, \infty)\).

Step4: Graph selection

We need a graph with an open circle at \(-7\) (because \(x > -7\), not \(x \geq -7\)) and the line shaded to the right of \(-7\). Looking at the options, option A has an open circle at \(-7\) (or around that area, considering the number line) and shading to the right.

Answer:

Set notation: \(\{x | x > -7\}\)
Interval notation: \((-7, \infty)\)
Correct graph: A