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, we simplify the inequality \(5x + 9 - 7x \leq 6\).

Step 1: Combine like terms

Combine the \(x\)-terms: \(5x - 7x = -2x\), so the inequality becomes \(-2x + 9 \leq 6\).

Step 2: Solve for \(x\)

Subtract 9 from both sides: \(-2x + 9 - 9 \leq 6 - 9\), which simplifies to \(-2x \leq -3\).
Divide both sides by \(-2\). Remember, when dividing by a negative number, the inequality sign flips. So we get \(x \geq \frac{3}{2}\) (or \(x \geq 1.5\)).

Now we test each value:

For \(x = 4\):

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

For \(x = 0\):

\(0 \geq 1.5\) is false. Substitute into the original inequality:
Left side: \(5(0) + 9 - 7(0) = 9\). \(9 \leq 6\) is false. So \(x = 0\) is False.

For \(x = -2\):

\(-2 \geq 1.5\) is false. Substitute into the original inequality:
Left side: \(5(-2) + 9 - 7(-2) = -10 + 9 + 14 = 13\). \(13 \leq 6\) is false. So \(x = -2\) is False.

For \(x = 1.5\):

\(1.5 \geq 1.5\) is true (since it's equal). Substitute into the original inequality:
Left side: \(5(1.5) + 9 - 7(1.5) = 7.5 + 9 - 10.5 = 6\). \(6 \leq 6\) is true. 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:

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