Answer
$(-∞,-\frac{7}{3}]$
Work Step by Step
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 $-\frac{7}{3}$.