Question

1. solve and graph the inequality:

\\(\frac{5}{4}b < 2\frac{2}{4}\\)

Explanation:

Step1: Convert mixed number to improper fraction

$2\frac{2}{4} = \frac{2\times4 + 2}{4} = \frac{10}{4}$

Step2: Isolate $b$ by multiplying reciprocal

Multiply both sides by $\frac{4}{5}$:
$\frac{4}{5} \times \frac{5}{4}b < \frac{10}{4} \times \frac{4}{5}$

Step3: Simplify both sides

$b < 2$

Step4: Graph explanation

Draw a number line. Place an open circle at 2 (since $b$ is strictly less than 2, not equal to it), then shade all the numbers to the left of 2.

Answer:

The solution to the inequality is $b < 2$.
For the graph: On a number line, use an open circle at $2$ and shade the region to the left of $2$.