Answer
The solution set is {x|x $\geq$ 21} , or [21,$\infty$) in interval notation.
Work Step by Step
Use the properties of inequalities to solve this inequality.
$\frac{2}{7}$x - $\frac{1}{4}$ $\geq$ $\frac{1}{4}$x + $\frac{1}{2}$
$\frac{2x}{7}$ - $\frac{1}{4}$ $\geq$ $\frac{x}{4}$ + $\frac{1}{2}$
Add $\frac{1}{4}$ to both sides.
$\frac{2x}{7}$ $\geq$ $\frac{x}{4}$ + $\frac{1}{2}$ + $\frac{1}{4}$
$\frac{2x}{7}$ $\geq$ $\frac{x+1}{4}$ + $\frac{1}{2}$
The least common multiple, or LCM, of 7, 4, and 2 is 28.
Multiply both sides by the LCM.
$\frac{2x}{7}$ $\times$ 28 $\geq$ $\frac{x+1}{4}$ $\times$ 28 + $\frac{1}{2}$ $\times$ 28
2x $\times$ 4 $\geq$ (x + 1) $\times$ 7 + 1 $\times$ 14
Use the distributive property.
8x $\geq$ 7x + 7 + 14
Subtract 7x from both sides.
x $\geq$ 21
The solution set is {x|x $\geq$ 21} , or [21,$\infty$) in interval notation.
