Question

an inequality is shown.
$3 (x + 13) > 18$
determine if each possible value for $x$ will make this inequality true or false.

	true	false
$-8$	$\circ$	$\circ$
$-6.5$	$\circ$	$\circ$

Explanation:

Step1: Solve the inequality for x

First, we solve the inequality \( 3(x + 13)>18 \). Divide both sides by 3:
\( \frac{3(x + 13)}{3}>\frac{18}{3} \)
Simplify to get \( x + 13>6 \). Then subtract 13 from both sides:
\( x+13 - 13>6 - 13 \)
So \( x>- 7 \).

Step2: Check \( x = - 7 \)

Substitute \( x=-7 \) into the inequality \( 3(x + 13)>18 \).
Left - hand side: \( 3(-7 + 13)=3\times6 = 18 \). But the inequality is \( 3(x + 13)>18 \), and \( 18\) is not greater than \( 18 \), so \( x = - 7 \) makes the inequality false.

Step3: Check \( x=-8 \)

Substitute \( x = - 8 \) into the inequality \( 3(x + 13)>18 \).
Left - hand side: \( 3(-8 + 13)=3\times5 = 15 \). Since \( 15<18 \), \( x=-8 \) makes the inequality false.

Step4: Check \( x=-6.5 \)

Substitute \( x=-6.5 \) into the inequality \( 3(x + 13)>18 \).
Left - hand side: \( 3(-6.5 + 13)=3\times6.5 = 19.5 \). Since \( 19.5>18 \), \( x = - 6.5 \) makes the inequality true.

Answer:

• For \( x=-7 \): False
• For \( x = - 8 \): False
• For \( x=-6.5 \): True