How do you solve -2( x - 4) \leq 3x?

2 Answers
Feb 21, 2017

x>=8/5

Explanation:

-2(x-4) <=3 x

Expand the parenthesis
-2 x + 8 <= 3 x

add 2 x both side.
2 x -2 x + 8 <= 3 x+ 2 x
8 <= 5 x

divide 5 to both side
8/5 <= (5 x)/5

8/5 <=x or x>=8/5

Feb 21, 2017

See the entire solution process below:

Explanation:

First, expand the terms within parenthesis:

(color(red)(-2) xx x) - (color(red)(-2) xx 4) <= 3x

-2x + 8 <= 3x

Next, add color(red)(2x) to each side of the inequality to isolate the x term while keeping the inequality balanced:

color(red)(2x) - 2x + 8 <= color(red)(2x) + 3x

0 + 8 <= (2 + 3)x

8 <= 5x

Now, divide each side of the inequality by color(red)(5) to solve for x while keeping the inequality balanced:

8/color(red)(5) <= (5x)/color(red)(5)

8/5 <= (color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5))

8/5 <= x

To put the solution in terms of x we can reverse or "flip" the inequality:

x >= 8/5