-4 + b/10 ≥ -3

Question image

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

  1. 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:

$$ \frac{b}{10} \geq 1 $$

  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:

$$ b \geq 10 $$

  1. 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).

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