Question

1. ( 8(1 - 8x) > -376 )

Explanation:

Step1: Divide both sides by 8

To simplify the inequality \(8(1 - 8x) > -376\), we divide both sides by 8. Since 8 is positive, the direction of the inequality sign remains the same.
\[
\frac{8(1 - 8x)}{8} > \frac{-376}{8}
\]
Simplifying both sides gives:
\[
1 - 8x > -47
\]

Step2: Subtract 1 from both sides

Next, we subtract 1 from both sides of the inequality \(1 - 8x > -47\) to isolate the term with \(x\).
\[
1 - 8x - 1 > -47 - 1
\]
Simplifying both sides gives:
\[
-8x > -48
\]

Step3: Divide both sides by -8

Now, we divide both sides of the inequality \(-8x > -48\) by -8. When dividing an inequality by a negative number, the direction of the inequality sign flips.
\[
\frac{-8x}{-8} < \frac{-48}{-8}
\]
Simplifying both sides gives:
\[
x < 6
\]

Answer:

The solution to the inequality \(8(1 - 8x) > -376\) is \(x < 6\). On the number line, this would be represented by an open circle at 6 and an arrow pointing to the left (towards values less than 6).