Question

Solve for b.
b–10
4
≥1 or
–
10b+19≥19
Write your answer as a compound inequality with integers.

Answer 1

To solve the compound inequalities, we will work on each inequality separately.

1. **First Inequality:**

\[
\frac{b - 10}{4} \geq 1
\]

Multiply both sides by 4:

\[
b - 10 \geq 4
\]

Add 10 to both sides:

\[
b \geq 14
\]

2. **Second Inequality:**

\[
-10b + 19 \geq 19
\]

Subtract 19 from both sides:

\[
-10b \geq 0
\]

Divide by -10 (remember to flip the inequality sign):

\[
b \leq 0
\]

Now we combine the two inequalities obtained:

\[
b \geq 14 \quad \text{or} \quad b \leq 0
\]

Thus, the solution as a compound inequality is:

\[
b \leq 0 \quad \text{or} \quad b \geq 14
\]

In interval notation, the solution can also be expressed as:

\[
(-\infty, 0] \cup [14, \infty)
\]