Question

solve the following equation (x-5)\4 = (3 + 4x) \3 - (x-3)\ 6​

Answer 1

Answer:

x = -3

Step-by-step explanation:

Multiply both sides of the equation by 12, the least common multiple of 4,3,6.

3(x−5)=4(3+4x)−2(x−3)

Use the distributive property to multiply 3 by x−5.

3x−15=4(3+4x)−2(x−3)

Use the distributive property to multiply 4 by 3+4x.

3x−15=12+16x−2(x−3)

Use the distributive property to multiply −2 by x−3.

3x−15=12+16x−2x+6

Combine 16x and −2x to get 14x.

3x−15=12+14x+6

Add 12 and 6 to get 18.

3x−15=18+14x

Subtract 14x from both sides.

3x−15−14x=18

Combine 3x and −14x to get −11x.

−11x−15=18

Add 15 to both sides.

−11x=18+15

Add 18 and 15 to get 33.

−11x=33

Divide both sides by −11.

x=  

−11

33

Divide 33 by −11 to get −3.

x=−3

Answer 2

$\sf \Large Solution!!$

$\sf \dfrac{x-5}{4}=\dfrac{3+4x}{3}-\dfrac{x-3}{6}$

$\sf \dfrac{x-5}{4}=\dfrac{2(3+4x)-x+3}{6}$

$\sf \dfrac{x-5}{4}=\dfrac{6+8x-x+3}{6}$

$\sf \dfrac{x-5}{4}=\dfrac{9+7x}{6}$

Cross multiplication.

$\sf 6(x-5)=4(9+7x)$

$\sf 6x-30=36+28x$

$\sf 6x-28x=30+36$

$\sf -22x=66$

$\sf x=\dfrac{66}{-22}$

$\sf x=-3$