Question

solve the linear inequality for w. write your answer in inequality notation. 6 > -4w + 10

Explanation:

Step1: Subtract 10 from both sides

To isolate the term with \( w \), we subtract 10 from both sides of the inequality \( 6 > -4w + 10 \).
\[
6 - 10 > -4w + 10 - 10
\]
Simplifying both sides gives:
\[
-4 > -4w
\]

Step2: Divide both sides by -4 (and reverse the inequality sign)

When dividing an inequality by a negative number, the direction of the inequality sign must be reversed. We divide both sides of \( -4 > -4w \) by -4.
\[
\frac{-4}{-4} < \frac{-4w}{-4}
\]
Simplifying both sides gives:
\[
1 < w
\]
Which can also be written as \( w > 1 \).

Answer:

\( w > 1 \)