Multiply the entire inequality by the least common multiple of the denominators (2 and 3), which is 6, to…

Question

Multiply the entire inequality by the least common multiple of the denominators (2 and 3), which is 6, to eliminate the fractions.

ScanSolve AI Tutor · Accepted Answer

here is the solution for the inequality:

\frac{1}{2}(x-1) - \frac{1}{3}(x+5) \le 1

Multiply the entire inequality by the least common multiple of the denominators (2 and 3), which is 6, to eliminate the fractions.
$6 \times \frac{1}{2}(x-1) - 6 \times \frac{1}{3}(x+5) \le 6 \times 1$ $3(x-1) - 2(x+5) \le 6$
Distribute the 3 and the $-2$ into their respective parentheses.
$3x - 3 - 2x - 10 \le 6$
Combine like terms on the left side.
$(3x - 2x) + (-3 - 10) \le 6$ $x - 13 \le 6$
Add 13 to both sides of the inequality to isolate $x$ .
$x \le 6 + 13$ $x \le 19$
The solution is:
$\boxed{x \le 19}$
Just one more to go! Send it over.

Multiply the entire inequality by the least common multiple of the denominators (2 and 3), which is 6, to eliminate the fractions.