Question

Solve the following inequality for bb. Write your answer in simplest form.
7, minus, left parenthesis, minus, 2, b, plus, 10, right parenthesis, is less than, 6, b, minus, 8, plus, 5
7−(−2b+10)<
6b−8+5

Answer 1

To solve the inequality \( 7 - (-2b + 10) < 6b - 8 + 5 \), we first simplify both sides.

1. Simplify the left side:
\[
7 - (-2b + 10) = 7 + 2b - 10 = 2b - 3
\]

2. Simplify the right side:
\[
6b - 8 + 5 = 6b - 3
\]

Now, rewrite the inequality:
\[
2b - 3 < 6b - 3
\]

3. Next, we want to isolate \( b \). To do this, we add \( 3 \) to both sides:
\[
2b < 6b
\]

4. Now, subtract \( 2b \) from both sides:
\[
0 < 4b
\]

5. Divide both sides by \( 4 \) (remember, since we're dividing by a positive number, the inequality direction stays the same):
\[
0 < b \quad \text{or} \quad b > 0
\]

Thus, the solution to the inequality is:
\[
\boxed{b > 0}
\]