# What is the solution to the inequality -6(4-x) <= -4(x+1)?

Aug 31, 2015

#### Answer:

$x \le 2$

#### Explanation:

Use the distributive property of multiplcation to expand the parantheses

$- 6 \cdot 4 - 6 \cdot \left(- x\right) \le - 4 \cdot x - 4 \cdot 1$

$- 24 + 6 x \le - 4 x - 4$

Rearrange the inequality to get a single $x$-term on one side

$6 x + 4 x \le - 4 + 24$

$10 x \le 20$

This is equivalent to

$x \le 2$

So, for any value of $x$ that is smaller than or equal to $2$, the inequality will be true. The solution set will thus be $\left(- \infty , 2\right]$.