Home > Algebra > Multi-Step Inequalities

How do you solve and graph #(2x)/3>4x+10#?

Answer 1

Hazel Anglin

#x<-3#

#(2x)/3>4x+10# (Multiply both sides by 3)

#2x>3(4x+10)# (Distribute 3 to numbers in bracket)

#2x>12x+30# (subtract 12x from both sides)

#-10x>30# (Divide both sides by -10)

#x>-3# (According to math rules, when dividing an inequality by a negative number, > becomes <)

#x<-3#

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

Answer 2

Avery Alexander

To solve and graph the inequality (2x)/3 > 4x + 10, follow these steps:

Multiply both sides of the inequality by 3 to eliminate the fraction: (2x > 12x + 30).
Subtract 12x from both sides: (-10x > 30).
Divide both sides by -10. Since you are dividing by a negative number, flip the direction of the inequality sign: (x < -3).

So, the solution to the inequality is (x < -3). To graph this on a number line, you would draw an open circle at -3 (since -3 is not included in the solution), and shade to the left, indicating all values of x less than -3.

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 #(2x)/3&gt;4x+10#?

How do you solve and graph #(2x)/3>4x+10#?