Sure, let's solve the inequality step by step:
1. Start with the given inequality:
[tex]\[
3 - (2x - 5) < -4(x + 2)
\][/tex]
2. Distribute and simplify each side:
- First, simplify inside the parentheses:
[tex]\[
2x - 5
\][/tex]
- Then distribute the negative sign:
[tex]\[
3 - 2x + 5 < -4(x + 2)
\][/tex]
- Combine like terms on the left side:
[tex]\[
8 - 2x < -4x - 8
\][/tex]
3. Isolate the variable [tex]\(x\)[/tex]:
- Add [tex]\(4x\)[/tex] to both sides to get all [tex]\(x\)[/tex] terms on one side:
[tex]\[
8 - 2x + 4x < -8
\][/tex]
- Simplify the expression:
[tex]\[
8 + 2x < -8
\][/tex]
- Subtract 8 from both sides:
[tex]\[
2x < -16
\][/tex]
- Divide by 2 to isolate [tex]\(x\)[/tex]:
[tex]\[
x < -8
\][/tex]
4. The solution to the inequality:
[tex]\[
x < -8
\][/tex]
Therefore, the solution set for the inequality [tex]\(3 - (2x - 5) < -4(x + 2)\)[/tex] is [tex]\( (-\infty, -8) \)[/tex].
