Answer
$(-\infty,\frac{3}{5}]$
Work Step by Step
$\frac{1}{4}(3x+2)-x\geq\frac{3}{8}(x-5)+2$
Mutiply both sides of the equation by 8, the least common multiple, to eliminate fractions.
$8(\frac{1}{4}(3x+2))-8(x)\geq8(\frac{3}{8}(x-5))+8(2)$
Simplify. Apply the distributive property. Combine like terms.
$2(3x+2)-8x\geq3(x-5)+16$
$6x+4-8x\geq3x-15+16$
$4-2x\geq3x+1$
Add 2x to each side of the equation. Subtract 1 from each side.
$4-2x+2x\geq3x+1+2x$
$4\geq5x+1$
$4-1\geq5x+1-1$
$3\geq5x$
Divide both sides by 5.
$3\div5\geq5x\div5$
$\frac{3}{5}\geq x$
$x\leq\frac{3}{5}$
This is written in interval notation as
$(-\infty,\frac{3}{5}]$
where ] indicates that $\frac{3}{5}$ is included in the solution set for x.