## Intermediate Algebra (6th Edition)

$(-∞,-\frac{7}{3}]$
We are given that $\frac{2}{5}(x-6)\geq x-1$. To solve for x, first simplify the left side by using the distributive property. $\frac{2}{5}x-\frac{12}{5}\geq x-1$ Add $\frac{12}{5}$ to both sides of the equation. $\frac{2}{5}x\geq x+\frac{7}{5}$ Subtract x from both sides. $-\frac{3}{5}x\geq\frac{7}{5}$ Multiply both sides by 5. $-3x\geq7$. Divide both sides by -3 (which will reverse the inequality sign). $x\leq-\frac{7}{3}$ Therefore, the inequality will be satisfied by all values of x that are less than or equal to $-\frac{7}{3}$.