-4 + b/10 ≥ -3
Understand the Problem
The question is asking to solve the inequality involving the variable b, and to interpret the results on the number line provided.
Answer
$b \geq 10$
Answer for screen readers
The solution to the inequality is $b \geq 10$.
Steps to Solve
- Isolate the variable term
To isolate the term containing $b$, add 4 to both sides of the inequality:
$$ -4 + \frac{b}{10} + 4 \geq -3 + 4 $$
This simplifies to:
$$ \frac{b}{10} \geq 1 $$
- Eliminate the fraction
Next, multiply both sides of the inequality by 10 to eliminate the fraction:
$$ 10 \cdot \frac{b}{10} \geq 10 \cdot 1 $$
This simplifies to:
$$ b \geq 10 $$
- Interpret the result on the number line
The solution $b \geq 10$ means that $b$ can be any number that is 10 or greater. On the number line, you would place a solid dot on 10 (indicating it is included) and shade the line to the right to show all values greater than 10.
The solution to the inequality is $b \geq 10$.
More Information
The inequality $b \geq 10$ indicates that any value of $b$ that is 10 or higher satisfies the original inequality. This means that all real numbers starting from 10 and moving rightward (e.g., 10, 11, 12, ...) are solutions.
Tips
- Forgetting to flip the inequality sign when multiplying or dividing by a negative number (not applicable here, since only positive numbers are used).