Answer
Solution in interval notation:
$[\frac{3}2,\frac{11}{2})$
See graph below.
Work Step by Step
We are asked to solve the inequality:
$3\le 4x - 3 \lt 19$
To obtain the solution, we need to isolate $x$.
We add $3$ to all sides:
$3+3\le 4x - 3 +3\lt 19+3$
$6\le 4x \lt 22$
Next, divide by $4$ and reduce:
$6\div 4\le 4x \div 4\lt 22\div 4$
$\frac{3}{2}\le x \lt \frac{11}{2}$
In interval notation, this can be written as:
$[\frac{3}2,\frac{11}{2})$
See the graph of the inequality below.
