how do you solve for the inequality ?−6x − 3 ≤ −4x + 1

Question

.

−6x − 3 ≤ −4x + 1

Answer 1

−6x − 3 ≤ −4x + 1

"To solve" means to find values of x that make the inequality true, so we must isolate x.

-6x ≤ -4x + 4 [add +3 to both sides retains sense of inequality]

-2x ≤ 4 [add +4x to both sides retains sense of inequality]

2x ≥ -4 [multiply by (-1) reverses the sense of the inequality]

x ≥ -2 [divide by +2 retains sense of inequality]

Check:

try (-5):

Is -6(-5) ≤ -4(-5) + 4 ?

30 ≤ 20 + 4 ?

30 ≤ 24 ? NO. check

try (0):

Is -6(0) ≤ -4(0) + 4 ?

0 ≤ 4 ? YES. check

Answer 2

-6x - 3 ≤ -4x + 1

-6x + 4x - 3 ≤ 1 Move all variables to one side of the inequality.

-6x + 4x ≤ 1 + 3 Move all constants to the other side of the inequality.

-2x ≤ 4

x ≥ 4 / (-2) When multiply or divide by a negative number, the inequality sign changes direction.

x ≥ -2