How do you solve #(2x-4)/6=-5x+2#?

Question

How do you solve #(2x-4)/6>=-5x+2#?

Kennedy Adams · Accepted Answer

See the entire solution process below:

First step, multiply each side of the inequality by #color(red)(6)# to eliminate the fraction: #color(red)(6) xx (2x - 4)/6 >= color(red)(6)(-5x + 2)# #cancel(color(red)(6)) xx (2x - 4)/color(red)(cancel(color(black)(6))) >= (color(red)(6) xx -5x) + (color(red)(6) xx 2)# #2x - 4 >= -30x + 12# Next step, add the necessary terms from each side of the inequality to isolate the #x# terms on one side of the inequality and the constants on the other side of the inequality while keeping the inequality balanced. #2x - 4 + color(red)(4) + color(blue)(30x) >= -30x + 12 + color(red)(4) + color(blue)(30x)# #2x + color(blue)(30x) - 4 + color(red)(4) >= -30x + color(blue)(30x) + 12 + color(red)(4)# #(2 + 30)x - 0 >= 0 + 16# #32x >= 16# Last step, divide each side of the inequality by #color(red)(32)# to solve for #x# while keeping the inequality balanced: #(32x)/color(red)(32) >= 16/color(red)(32)# #(color(red)(cancel(color(black)(32)))x)/cancel(color(red)(32)) >= 1/2# #x >= 1/2#

Julia Adams · Answer

undefined To solve the inequality (2x - 4) / 6 ≥ -5x + 2, follow these steps:

1. Multiply both sides of the inequality by 6 to eliminate the denominator:
   (2x - 4) ≥ -30x + 12

2. Distribute the -30x:
   2x - 4 ≥ -30x + 12

3. Add 30x to both sides to isolate the x terms on one side of the inequality:
   32x - 4 ≥ 12

4. Add 4 to both sides to isolate the x term:
   32x ≥ 16

5. Divide both sides by 32 to solve for x:
   x ≥ 16/32

6. Simplify:
   x ≥ 1/2

So, the solution to the inequality is x ≥ 1/2.

How do you solve #(2x-4)/6&gt;=-5x+2#?

How do you solve #(2x-4)/6>=-5x+2#?