Question

What is the solution to the inequality 5.25 – b ≥ 6.5? A number line going from negative 5 to positive 5. A solid circle appears between negative 1 and negative 2. The number line is shaded from the circle to negative 5. A number line going from negative 5 to positive 5. An open circle appears between negative 1 and negative 2. The number line is shaded from the circle to negative 5. A number line going from negative 5 to positive 5. A solid circle appears between negative 1 and negative 2. The number line is shaded from the circle to positive 5. A number line going from negative 5 to positive 5. An open circle appears between negative 1 and negative 2. The number line is shaded from the circle to positive 5.

Answer 1

Given:

The inequality is

$5.25-b\geq 6.5$

To find:

The solution of the given inequality on the number line.

Solution:

We have,

$5.25-b\geq 6.5$

Subtract 5.25 from both sides.

$5.25-b-5.25\geq 6.5-5.25$

$-b\geq 1.25$

Multiply both sides by -1 and change the sign of inequality.

$b\leq -1.25$

The value of b always less than or equal to -1.25. Since -1.25 included in the solution set, therefore there is a solid circle on -1.25.

-1.25 lies between -2 and -1. It means the solid circle lies between -1 and -2.

$b\leq -1.25$, so the number line is shaded from the circle to negative 5.

A number line going from negative 5 to positive 5 is the required solution if a solid circle appears between negative 1 and negative 2. The number line is shaded from the circle to negative 5.

Therefore, the correct option is A.