Let's solve the inequality step-by-step:
1. The given inequality is:
[tex]\[
-7(-4 + x) > -35
\][/tex]
2. Distribute the [tex]\(-7\)[/tex] on the left side of the inequality:
[tex]\[
-7 \cdot (-4 + x) = -7(-4) + (-7)x = 28 - 7x
\][/tex]
Now, the inequality becomes:
[tex]\[
28 - 7x > -35
\][/tex]
3. Subtract 28 from both sides to isolate the term involving [tex]\(x\)[/tex]:
[tex]\[
28 - 7x - 28 > -35 - 28
\][/tex]
Simplifying this, we get:
[tex]\[
-7x > -63
\][/tex]
4. Now, divide both sides by [tex]\(-7\)[/tex]. Remember that when you divide or multiply both sides of an inequality by a negative number, you must flip the inequality sign:
[tex]\[
\frac{-7x}{-7} < \frac{-63}{-7}
\][/tex]
Simplifying this, we get:
[tex]\[
x < 9
\][/tex]
So, the solution to the inequality [tex]\( -7(-4 + x) > -35 \)[/tex] is:
[tex]\[
x < 9
\][/tex]
