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
$-8$	$\circ$	$\circ$
$-6.5$	$\circ$	$\circ$
$-4$	$\circ$	$\circ$

Explanation:

Step1: Simplify the inequality

First, divide both sides by 3:
$\frac{3(x+13)}{3} > \frac{18}{3}$
$x + 13 > 6$
Then subtract 13 from both sides:
$x > 6 - 13$
$x > -7$

Step2: Test x=-7

$-7 > -7$ is false? No, wait: the simplified inequality is $x > -7$. Since $-7$ is not greater than $-7$, but wait substitute original: $3(-7+13)=3(6)=18$, $18>18$ is false? Wait no, correction:
Wait original substitution for x=-7:
$3(-7 + 13) = 3(6) = 18$. The inequality is $18>18$, which is false? Wait no, wait simplified inequality: $3(x+13)>18$ → $x+13>6$ → $x> -7$. So values greater than -7 make it true, values less than or equal make it false.

Step3: Test x=-8

$-8 > -7$ is false. Substitute original: $3(-8+13)=3(5)=15$, $15>18$ is false.

Step4: Test x=-6.5

$-6.5 > -7$ is true. Substitute original: $3(-6.5+13)=3(6.5)=19.5$, $19.5>18$ is true.

Step5: Test x=-4

$-4 > -7$ is true. Substitute original: $3(-4+13)=3(9)=27$, $27>18$ is true.

Wait correction on x=-7: $3(-7+13)=18$, and $18>18$ is false. So x=-7 is False. I made an error earlier. Correct answer:

Step1: Simplify the inequality

Divide by 3, subtract 13:

$$\begin{align*} 3(x+13)&>18\\ x+13&>6\\ x&>-7 \end{align*}$$

Step2: Check x=-7

$-7 > -7$ is false.

Step3: Check x=-8

$-8 > -7$ is false.

Step4: Check x=-6.5

$-6.5 > -7$ is true.

Step5: Check x=-4

$-4 > -7$ is true.

Answer:

-7: True
-8: False
-6.5: True
-4: True