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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 as {x|}
the solution is expressed in interval notation as
choose the correct graph of the solution set below.

Explanation:

Step1: Expand the left - hand side

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

Step2: Add 8 to both sides

Add 8 to isolate the term with \(x\). \(-2x-8 + 8\lt4 + 8\), 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 inequality sign flips. \(\frac{-2x}{-2}\gt\frac{12}{-2}\), so \(x\gt - 6\).

Answer:

• Set notation: \(\{x|x\gt - 6\}\)
• Interval notation: \((-6,\infty)\)
• The correct graph is A (assuming in graph A, there is an open circle at - 6 and the line extends to the right towards positive infinity).