solving inequaities

Question

3-4(3x-4)≥3(2-3x)

i understand the concept but keep getting weird answers

Answer 1

Hi Abi, solving inequalities is not much different than solving equalities.

 

3 - 4 * (3x - 4) ≥ 3 * (2 - 3x)

 

Clear parenthesis:

 

3 - 12x + 16 ≥ 6 - 9x

 

Get the numbers on one side and the variables on the other side:

 

Subtract 6 from both sides:

 

13 - 12x ≥ -9x

 

Add 12x to both sides:

 

13 ≥ 3x

 

Divide both sides by 3:

 

13/3 ≥ x

 

Answer: x ≤ 13/3

 

Check:

 

Substitute for x:

 

Let x = 13/3.

 

3 - 4 * (3 * 13/3 - 4) ≥ 3 * (2 - 3 * 13/3)

 

3 - 4 * (13 - 4) ≥ 3 * (2 - 13)

 

3 - 4 * 9 ≥ 3 * -11

 

3 - 36 ≥ -33

 

-33 ≥ -33, checks.

 

Now check for x = 14/3

 

3 - 4 * (3 * 14/3 - 4) ≥ 3 * (2 - 3 * 14/3)

 

3 - 4 * (14 - 4) ≥ 3 * (2 - 14)

 

3 - 4 * 10 ≥ 3 * -12

 

3 - 40 ≥ -36

 

-37 ≥ - 36, which is false.

 

Now check x = 12/3, or x = 4.

 

3 - 4 * (3 * 4 - 4) ≥ 3 * (2 - 3 * 4)

3 - 4 * (12 - 4) ≥ 3 * (2 - 12)

3 - 4 * 8 ≥ 3 * -10

3 - 32 ≥ -30

-29 ≥ - 30, which is true.

 

Questions?