Question

What are the solutions of the inequality? 12x – 3x + 11 > 4x – (17 – 9x)
A. x > –7
B. x < 7
C.x < - 14/11
D.x > -14/11

Answer 1

x
The problem to solve is:

12x - 3x + 11›4x - ( 17-9x)

First, let's work on the left hand side of your inequality, the 12x - 3x + 11
This means, for instance, to see if it can be simplified at all.
Multiply x and 12

Multiply x and 1

The x just gets copied along.

The answer is x

x

12*x evaluates to 12x

Multiply x and 3

Multiply x and 1

The x just gets copied along.

The answer is x

x

3*x evaluates to 3x

12*x-3*x evaluates to 9x

12*x-3*x+11 evaluates to 9x+11

So, all-in-all, the left hand side of your inequality can be written as: 9x+11
Now, let's work on the right hand side of your inequality, the 4x - ( 17-9x)
Multiply x and 4

Multiply x and 1

The x just gets copied along.

The answer is x

x

4*x evaluates to 4x

Multiply x and 9

Multiply x and 1

The x just gets copied along.

The answer is x

x

9*x evaluates to 9x

17-9*x evaluates to 17-9x

4x - -9x = 13x

The answer is 13x-17

4*x-(17-9*x) evaluates to 13x-17

The right hand side of your inequality can be written as: 13x-17
So with these (any) simplifications, the inequality we'll set out to solve is:
9x+11 › 13x-17

Move the 11 to the right hand side by subtracting 11 from both sides, like this:

From the left hand side:
11 - 11 = 0

The answer is 9x

From the right hand side:
-17 - 11 = -28

The answer is -28+13x


Now, the inequality reads:
9x › -28+13x

Move the 13x to the left hand side by subtracting 13x from both sides, like this:
From the left hand side:
9x - 13x = -4x

The answer is -4x

From the right hand side:
13x - 13x = 0

The answer is -28


Now, the inequality reads:
-4x › -28
To isolate the x, we have to divide both sides of the inequality by the other "stuff" (variables or coefficients)
around the x on the left side of the inequality.
The last step is to divide both sides of the inequality by -4 like this:

To divide x by 1

The x just gets copied along in the numerator.

The answer is x

-4x ÷ -4 = x

-28 ÷ -4 = 7

Note! Here's an important point about inequalities:

We are now dividing by -4, which is a number less than zero! This changes the form of your inequality. Or, in other words, your › will now become a ‹.
The solution to your inequality is:
x ‹ 7

So, your solution is:

x must be less than 7