# (3x − 2)/6 − (4x + 1)/4 = −2?

what is x? I got 3.83 and it was marked wrong

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• Multiply everything by 12 to get rid of fractions:

2(3x-2) - 3(4x+1) = -24   so now distribute:

6x -4 -12x -3 = -24   now combine:

-6x -7 = -24   now add 7

-6x = -17,   now divide by -6

x = 17/6 or around 2.8333

• (3x − 2)/6 − (4x + 1)/4 = −2

4(3x - 2) - 6(4x + 1) = -2(4)(6)

12x - 8 - 24x - 6 = - 48

-12x - 14 = -48

12x + 14 = 48

12x = 34

x = 34/12

x = 2 10/12 = 2 5/6 = (2.83333.....)

• Let solve it

(3x − 2)/6 − (4x + 1)/4 = −22(3x − 2) − 3(4x + 1) = −24− 6x = −17x ≈ 2.8333Thus x is 2.8333

•  3x - 2...........4x + 1

[----------- -  --------------= - 2]24

....6.................... 4

4(3x - 2) - 6(4x + 1) = - 48

12x - 8 - 24x - 6 = - 48

- 12x - 14 = - 48

- 12x = - 48 + 14

- 12x = - 34

• (3x − 2)/6 − (4x + 1)/4 = −2

2(3x − 2) − 3(4x + 1) = −24

6x = 17

x = 2.833..

• Lets try a graphic image solution • (3x − 2)/6 − (4x + 1)/4 = −2

2(3x − 2) − 3(4x + 1) = −24

− 6x = −17

x ≈ 2.8333

• My first thought is you had the right answer, but you rounded to 2DP.  Unless told to do so you should keep the result as a fraction.

(3x - 2) / 6 - (4x + 1) / 4 = -2

Multiply both sides by 12 (the LCD) to remove the fractions:

2(3x - 2) - 3(4x + 1) = -24

Expand the left side and combine like terms:

6x - 4 - 12x - 3 = -24

-6x - 7 = -24

-6x = -17

Divide both sides by -6:

x = 17/6

So you did something to be off by 1.  (17/6 = 2.83 rounded to 2DP), but either way the answer should be left as a simplified fraction.

• Multiply both sides by the lowest common denominator of 12 to get rid of fractions:

2(3x - 2) - 3(4x + 1) = -24

6x - 4 - 12x - 3 = -24

Group like terms:

6x - 12x = -24 + 4 + 3

-6x = -17

Divide both sides by -6:

x = -17/-6

x = 17/6 or 2⅚

That's the exact answer as a fraction. Even if you allow for a decimal equivalent, the answer would be 2.83333... which is still not what you wrote.

I think you must have switched a sign somewhere in your calculation. Double-check your work.

(3x - 2)/6 - (4x + 1)/4 = -2

(3(17/6) - 2)/6 - (4(17/6) + 1)/4 =? -2

(17/2 - 2)/6 - (34/3 + 1)/4 =? -2

(17/2 - 4/2)/6 - (34/3 + 3/3)/4 =? -2

(13/2)/6 - (37/3)/4 =? -2

13/12 - 37/12 =? -2

-24/12 =? -2

-2 = -2 ✓

x = 17/6 or 2⅚ or 2.83333...

• (3x − 2)/6 − (4x + 1)/4 = -2

2/2 * (3x - 2)/6 - 3/3 * (4x + 1)/4 = -2

(6x - 4)/12 - (12x - 3)/12 = -2

(6x - 4 - 12x + 3)/12 = -2

(-6x - 1)/12 = -2

-6x - 1 = -24

-6x = -23

x = -23/-6 = 3.83