Solve the inequality |2-3x| ≤ 11

|2-3x| < 11

3|x-2/3| < 11

|x-2/3| < 11/3

The distance of x from 2/3 is less than 11/3.

<---O========+=========O--->

-9/3 2/3 13/3

-3 < x < 13/3

Solve the inequality |2-3x| ≤ 11

Tutors, please sign in to answer this question.

Westford, MA

|2-3x| < 11

3|x-2/3| < 11

|x-2/3| < 11/3

The distance of x from 2/3 is less than 11/3.

<---O========+=========O--->

-9/3 2/3 13/3

-3 < x < 13/3

Middletown, CT

Hi Kay;

In the title, you explain this is <.

In the description, you explain this is ≤.

I will use the first...

|2-3x| < 11

Absolute value is always positive.

(2-3x) can be either...

+(2-3x) or -(2-3x).

When the absolute value of either is taken, it has the same result.

-(2-3x)<11

-2+3x<11

Let's add 2 to both sides...

-2+2+3x<11+2

3x<13

Divide both sides by 3...

(3x)/3<13/3

x<13/3

+(2-3x)<11

2-3x<11

Let's subtract 2 from both sides...

2-2-3x<11-2

-3x<9

Divide both sides by -3. Because this is a negative number < will switch to >...

(-3x)/-3>9/-3

x>-3

-3<x<13/3

Let's verify by plugging-in a few points within this domain...

|2-3x| < 11

x=0

|2-[(3)(0)]|<11

|2|<11

2<11-----YES

x=-1

|2-3x| < 11

|2-[(3)(-1)]|<11

|2+3|<11

5<11---YES

x=1

|2-3x| < 11

|2-[(3)(1)]|<11

|2-3|<11

-1<11-------YES

Let's verify by plugging-in a few points outside of this domain...

x=-4

|2-3x| < 11

|2-[(3)(-4)]|<11

|2+12|<11

13<11-----NO

x=5

|2-3x| < 11

|2-[(3)(5)]|<11

|2-15|<11

|-13|<11

13<11-------NO

Evan F.

Mathematics graduate looking to enhance your mathematics ability.

Cambria Heights, NY

4.9
(315 ratings)

John P.

Tutor of math and physics, recent college graduate

Short Hills, NJ

5.0
(20 ratings)

- Math 9678
- Calculus 2180
- Algebra 2 3417
- Math Help 5356
- Trigonometry 1501
- Algebra 1 4018
- Sequences 118
- Series 61
- Precalculus Homework 346
- Prealgebra 170