Home > Algebra > Multi-Step Inequalities

How do you solve and graph #3[4x-(2x-7)]<2(3x-5)#?

Answer 1

#x in O/#
That is there is no value of #x# for which the given inequality is true.

Given #color(white)("XXX")3[4x-(2x-7)] < 2(3x-5)#

First, simplify both the left and right sides: #color(white)("XXX")3[2x+7] < 6x-10#

#color(white)("XXX")6x+21 < 6x -10#

Since we can subtract the same amount from both sides without effecting the validity or orientation of the inequality we have #color(white)("XXX")21 < -10#

which is clearly not true for any value of #x#

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

Answer 2

Julia Adams

To solve and graph the inequality 3[4x-(2x-7)] < 2(3x-5), follow these steps:

Distribute and simplify both sides of the inequality: 3[4x - (2x - 7)] < 2(3x - 5) 3[4x - 2x + 7] < 6x - 10 3[2x + 7] < 6x - 10 6x + 21 < 6x - 10
Subtract 6x from both sides to isolate the constant term: 6x - 6x + 21 < 6x - 6x - 10 21 < -10
Since 21 is never less than -10, the inequality is false for all values of x.

Therefore, the solution to the inequality is an empty set, and there is no solution when graphed on the coordinate plane.

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.

How do you solve and graph #3[4x-(2x-7)]&lt;2(3x-5)#?

How do you solve and graph #3[4x-(2x-7)]<2(3x-5)#?