Question

an inequality is shown.
$5x + 9 - 7x \leq 6$
determine if each possible value for $x$ will make this inequality true or false.

	true	false
0	$\circ$	$\circ$
$-2$	$\circ$	$\circ$
$1.5$	$\circ$	$\circ$

Explanation:

First, simplify the inequality \(5x + 9 - 7x \leq 6\). Combine like terms: \( -2x + 9 \leq 6\). Then subtract 9 from both sides: \( -2x \leq -3\). Divide both sides by -2 (remember to reverse the inequality sign): \(x \geq \frac{3}{2}\) or \(x \geq 1.5\).

Step 1: Test \(x = 4\)

Substitute \(x = 4\) into the original inequality: \(5(4) + 9 - 7(4) = 20 + 9 - 28 = 1\). Since \(1 \leq 6\) is true, and \(4 \geq 1.5\), so \(x = 4\) is True.

Step 2: Test \(x = 0\)

Substitute \(x = 0\) into the original inequality: \(5(0) + 9 - 7(0) = 9\). Since \(9 \leq 6\) is false, and \(0 < 1.5\), so \(x = 0\) is False.

Step 3: Test \(x = -2\)

Substitute \(x = -2\) into the original inequality: \(5(-2) + 9 - 7(-2) = -10 + 9 + 14 = 13\). Since \(13 \leq 6\) is false, and \(-2 < 1.5\), so \(x = -2\) is False.

Step 4: Test \(x = 1.5\)

Substitute \(x = 1.5\) into the original inequality: \(5(1.5) + 9 - 7(1.5) = 7.5 + 9 - 10.5 = 6\). Since \(6 \leq 6\) is true, and \(1.5 = 1.5\), so \(x = 1.5\) is True.

Answer:

• For \(x = 4\): True
• For \(x = 0\): False
• For \(x = -2\): False
• For \(x = 1.5\): True

(To mark in the table:

• Row \(x = 4\): Select True
• Row \(x = 0\): Select False
• Row \(x = -2\): Select False
• Row \(x = 1.5\): Select True)