Question

solve the compound inequality.

(4x + 1 > -7) or (2x - 3 < -15)

graph the solution on the number line.

Explanation:

Solve the first inequality

Using the Compound Inequalities knowledge point

$$
LATEXBLOCK0
$$

Solve the second inequality

Using the Compound Inequalities knowledge point

$$
LATEXBLOCK1
$$

Combine the solutions

Using the Compound Inequalities knowledge point

$$ x < -6 \quad \text{or} \quad x > -2 $$

In interval notation, this is written as:

$$ (-\infty, -6) \cup (-2, \infty) $$

Graph the solution on a number line

Using the Inequality Graphing knowledge point

• Plot an open circle at \(x = -6\) and shade to the left.
• Plot an open circle at \(x = -2\) and shade to the right.

Answer:

The solution to the compound inequality is:

$$ x < -6 \quad \text{or} \quad x > -2 $$

In interval notation:

$$ (-\infty, -6) \cup (-2, \infty) $$