Question

What is the solution of the inequality below for y ?

2x − 5y ≤ 15

Answer 1

The solution for y in 2x − 5y ≤ 15  is $y \geq \frac{2x}{5} - 3$

Solution:

Given that we have to find solution for given inequality for y

2x − 5y ≤ 15

Let us solve above equation for "y"

$2x - 5y \leq 15$

Add -2x on both sides

$-2x + 2x - 5y\leq 15 - 2x\\\\-5y \leq 15 - 2x$

Divide by -5 on both sides

Remember that You can perform on operations on both sides of inequality, and have its truth value unchanged

But if we multiply or divide by a negative number, we must flip the sign

$\frac{-5y}{-5} \geq \frac{15}{-5} - \frac{2x}{-5}\\\\y \geq -3 + \frac{2x}{5}\\\\y \geq \frac{2x}{5} - 3$

Thus solution for "y" is found