Question

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

Answer 1

x = -43/6

Explanation:

To solve this equation, you solve for 'x' by isolating it. This means to move every other number to the other side of 'x'. You can move numbers when they 'cancel' out by doing the opposite (Adding and subtracting are opposites. Dividing and multiplying are opposites).

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

`(3x-2)/(6)*(2)/(2)-(4x+1)/(4)*(3)/(3) = 3` Multiply each fraction by a fraction that equals '1'. (2/2 = 1 and 3/3 = 1). This will give them a common denominator.

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

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

`((6x-4)-(12x+3))/(12)= 3` Combine the fractions with the same denominator

`((6x-4)-12x-3)/(12)= 3` Subtract binomials. -(12x+3) is -12x-3

`(6x-4-12x-3)/(12)= 3` Remove unnecessary brackets

`(-6x-7)/(12)= 3` Combined like terms.

`(-(6x+7))/(12)= 3` Factor out the negative in the top.

`-(6x+7)= 3*12` Multiplied both sides by 12

`-(6x+7)= 36` Simplified right side

`6x+7= -36` Divided both sides by -1

`6x= -36-7` Subtract 7 from both sides

`6x= -43` Simplified right side

`x= (-43)/(6)` Divided both sides by 6. Answer in fraction form.

x = 7.166..67 Answer in decimal form

Therefore x is -43/6 or about 7.17.