Question

for each value of x, determine whether it is a solution to -5 - 8x > -53.

x	is it a solution?
6	yes (○)	no (○)
8	yes (○)	no (○)
-2	yes (○)	no (○)

Explanation:

First, we solve the inequality \(-5 - 8x > -53\) for \(x\).

Step 1: Add 5 to both sides

Add 5 to each side of the inequality to isolate the term with \(x\).

$$ -5 - 8x + 5 > -53 + 5 $$

Simplifying both sides, we get:

$$ -8x > -48 $$

Step 2: Divide by -8 (and reverse inequality)

Divide both sides by -8. Remember, when dividing an inequality by a negative number, we reverse the inequality sign.

$$ \frac{-8x}{-8} < \frac{-48}{-8} $$

Simplifying, we find:

$$ x < 6 $$

Now we check each value of \(x\) to see if it satisfies \(x < 6\):

• For \(x = -9\): \(-9 < 6\) is true, so it is a solution.
• For \(x = 6\): \(6 < 6\) is false, so it is not a solution.
• For \(x = 8\): \(8 < 6\) is false, so it is not a solution.
• For \(x = -2\): \(-2 < 6\) is true, so it is a solution.

Answer:

\(x\)	Is it a solution?
\(6\)	No
\(8\)	No
\(-2\)	Yes