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 as

the solution is expressed in interval notation as

choose the correct graph of the solution set below

Explanation:

Step1: Solve the inequality

Given \(2(x + 4)<16\). First, distribute the \(2\) on the left - hand side: \(2x+8 < 16\). Then, subtract \(8\) from both sides: \(2x+8 - 8<16 - 8\), which simplifies to \(2x<8\). Next, divide both sides by \(2\): \(\frac{2x}{2}<\frac{8}{2}\), so \(x < 4\).

Step2: Write the set - notation

The set - notation for \(x < 4\) is \(\{x|x < 4\}\).

Step3: Write the interval - notation

The interval - notation for \(x < 4\) is \((-\infty,4)\).

Step4: Analyze the graph

The graph of \(x < 4\) is a number line with an open circle at \(4\) (since \(4\) is not included in the solution set) and an arrow pointing to the left (towards \(-\infty\)).

Answer:

• The solution in set notation is \(\{x|x < 4\}\).
• The solution in interval notation is \((-\infty,4)\).
• The correct graph is the one with an open circle at \(4\) and an arrow to the left (assuming option B or D is of this form, but based on standard graphing of \(x < 4\), it's the graph that has an open - dot at \(4\) and shading to the left).