Answer :

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]