Home > Algebra > Multi-Step Inequalities

How do you solve #-4/5(x-3)≤-12#?

Answer 1

#x >= 18#

Treat inequalities in exactly the same way as an equation unless you are are multiplying or dividing by a negative number. In this case the inequality sign has to change around. Also do not cross-multiply across an inequality.

Let's get rid of the annoying fraction outside the bracket by multiplying by #5/4#, leaving the minus sign there for now.

#color(red)(5/4) xx-4/5(x-3)<= color(red)(5/4) xx-12#

#=-(x-3) <=-15 " Multiplying out gives" #

#" "=-x +3 <=-15#

The problem now is the #-x#. The easiest is to move it to the right side to make it positive ;

#15 + 3 <=x#

#18 <= x# which can also be written as #x >= 18#

The other method would involve dividing by -1. #-x <=-15 -3# #-x <=-18 " divide by -1 "rArr" sign will change"#

#x >= 18#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Kennedy Adams

To solve the inequality -4/5(x-3) ≤ -12, we can begin by isolating the variable x. First, we multiply both sides of the inequality by -5/4 to eliminate the fraction: -5/4 * -4/5(x-3) ≤ -5/4 * -12 This simplifies to: (x-3) ≥ 15 Next, we add 3 to both sides of the inequality to isolate x: x ≥ 15 + 3 x ≥ 18 So, the solution to the inequality is x ≥ 18.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.