Certainly! Let's solve the inequality step-by-step:
1. Distribute the constants inside the parentheses:
[tex]\[
5(x - 7) - 2(3 - x)
\][/tex]
Distributing the [tex]\(5\)[/tex]:
[tex]\[
5 \cdot x - 5 \cdot 7 = 5x - 35
\][/tex]
Distributing the [tex]\(-2\)[/tex]:
[tex]\[
-2 \cdot 3 + (-2) \cdot (-x) = -6 + 2x
\][/tex]
Now, combine these results:
[tex]\[
5x - 35 - 6 + 2x
\][/tex]
2. Combine like terms:
[tex]\[
5x + 2x - 35 - 6
\][/tex]
Adding the [tex]\(x\)[/tex] terms together and the constant terms together:
[tex]\[
7x - 41
\][/tex]
3. Set up the inequality:
[tex]\[
7x - 41 < 8
\][/tex]
4. Isolate the [tex]\(x\)[/tex] term:
Add 41 to both sides:
[tex]\[
7x - 41 + 41 < 8 + 41
\][/tex]
Simplifying, we have:
[tex]\[
7x < 49
\][/tex]
5. Solve for [tex]\(x\)[/tex]:
Divide both sides by 7:
[tex]\[
x < \frac{49}{7}
\][/tex]
Simplifying the fraction:
[tex]\[
x < 7
\][/tex]
So, the solution to the inequality [tex]\(5(x-7) - 2(3-x) < 8\)[/tex] is:
[tex]\[
x < 7
\][/tex]
