+128731 Find x when -1/2(2x-3)+1/3(4-6x)=1/4(7-2x)-3
OK...to make things a little easier, let's multiply through by the common denominator of 2, 3 and 4, namely - 12. Doing this will get rid of those pesky fractions !!
So we have
(12)*(-1/2)(2x-3)+(12)*(1/3)(4-6x)=(12)*(1/4)(7-2x)-3 =
-6(2x-3) + 4(4-6x) = 3(7-2x) -3 ...... Now, let's "distribute" the "coefficients" outside each parenthesis "across" the terms inside.....this gives....
-12x + 18 + 16 - 24x = 21 -6x - 3 Now.....combining "like" terms, we have
-36x + 34 = 18 - 6x ......add 36x to each side
34 = 18 + 30x .......subtract 18 from both sides....this gives
16 = 30x
Now dividing by 30 on both sides, we have
x = 16/30 which reduces to 8/15
Now, let's check our answer using this....-6(2x-3) + 4(4-6x) = 3(7-2x) -3 so we have
-6(2(8/15) -3) + 4 (4 -6(8/15)) = 3(7- 2(8/15)) - 3 ???
-96/15 + 18 + 16 - 192/15 = 21 - 48/15 - 3 ???
-288/15 + 34 = 18 - 48/15 ???
16 = 240/15 ???
16 = 16 .......√ √ √
And we're finished !!!
