Question

solve the inequality. express your answer using set notation and interval notation. graph the solution set. -4(x + 3) < 16
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
a. graph option a
b. graph option b
c. graph option c
d. graph option d

Explanation:

Step1: Divide both sides by -4

When dividing an inequality by a negative number, the inequality sign flips. So, divide both sides of \(-4(x + 3) < 16\) by \(-4\):
\(\frac{-4(x + 3)}{-4} > \frac{16}{-4}\)
Simplifies to: \(x + 3 > -4\)

Step2: Subtract 3 from both sides

Subtract 3 from both sides of \(x + 3 > -4\):
\(x + 3 - 3 > -4 - 3\)
Simplifies to: \(x > -7\)

Step3: Set Notation

In set notation, the solution is \(\{x | x > -7\}\)

Step4: Interval Notation

In interval notation, this is \((-7, \infty)\)

Step5: Graph Selection

The graph should have an open circle at \(-7\) (since \(x > -7\), not \(x \geq -7\)) and an arrow pointing to the right (for values greater than \(-7\)). Looking at the options, Option B matches this (open circle at \(-7\), arrow right).

Answer:

Set notation: \(\{x | x > -7\}\)
Interval notation: \((-7, \infty)\)
Graph: B