Answer
The solution is $\Big[1,\dfrac{11}{3}\Big]$
Work Step by Step
$|7-3x|\le4$
Solving this absolute value inequality is equivalent to solving the following inequality:
$-4\le7-3x\le4$
$\textbf{Solve the inequality shown above:}$
$-4\le7-3x\le4$
Subtract $7$ from all three parts of the inequality:
$-4-7\le7-7-3x\le4-7$
$-11\le-3x\le-3$
Divide all three parts of the inequality by $-3$ and reverse the inequality signs:
$\dfrac{-11}{-3}\ge\dfrac{-3x}{-3}\ge\dfrac{-3}{-3}$
$\dfrac{11}{3}\ge x\ge1$
Expressing the solution in interval notation:
$\Big[1,\dfrac{11}{3}\Big]$
