Question

graph the compound inequality representing the statement the sum of -4x and 6 is no fewer than -18 or 2x plus 8 is at least 38.

Explanation:

Step1: Translate the statements into inequalities

• The sum of \(-4x\) and \(6\) is no fewer than \(-18\): \(-4x + 6\geq - 18\).
• \(2x\) plus \(8\) is at least \(38\): \(2x+8\geq38\).

Step2: Solve the first inequality \(-4x + 6\geq - 18\)

Subtract \(6\) from both sides: \(-4x\geq-18 - 6\), so \(-4x\geq-24\).
Divide both sides by \(- 4\) (and reverse the inequality sign): \(x\leq6\).

Step3: Solve the second inequality \(2x + 8\geq38\)

Subtract \(8\) from both sides: \(2x\geq38 - 8\), so \(2x\geq30\).
Divide both sides by \(2\): \(x\geq15\).

Answer:

The solution of the compound inequality \(x\leq6\) or \(x\geq15\) is graphed as a number - line with a closed circle at \(x = 6\) (since \(x = 6\) is included in \(x\leq6\)) and shading to the left of \(6\), and a closed circle at \(x = 15\) (since \(x = 15\) is included in \(x\geq15\)) and shading to the right of \(15\).