Answer
$[-26\frac{1}{3},\infty)$
Work Step by Step
$\frac{5x+1}{7}-\frac{2x-6}{4}\geq-4$
Solve for x.
Multiply each side of the equation by 28 to convert the fractions to whole numbers.
$28\times(\frac{5x+1}{7}-\frac{2x-6}{4})\geq-4\times28$
Apply the distributive property.
$4(\frac{5x+1}{7})-7(\frac{2x-6}{4})\geq-112$
Apply the distributive property again.
$20x+4-(14x-42)\geq-112$
Simplify.
$6x+46\geq-112$
Subtract 46 from each side.
$6x+46\geq-112$
$6x+46-46\geq-112-46$
$6x\geq-158$
$x\geq-26.3\overline3$
$x\geq-26\frac{1}{3}$
In interval notation this is written as
$[-26\frac{1}{3},\infty)$
where [ indicates that the solution set for x includes $-26\frac{1}{3}$.
