To solve the compound inequalities, we will work on each inequality separately.
-
First Inequality:
\[ \frac{b - 10}{4} \geq 1 \]
Multiply both sides by 4:
\[ b - 10 \geq 4 \]
Add 10 to both sides:
\[ b \geq 14 \]
-
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:
\[ (-\infty, 0] \cup [14, \infty) \]
1 answer