Question

Solve the equation
3x-2
4
-
2x - 5- 1 + x
3 6

Answer 1

• 
  `\boxed{\sf x=12}`

Explanation:

`\sf \cfrac{3x-2}{4}-\cfrac{2x-5}{3}=\cfrac{1+x}{6}`

First, let's find the LCM of 4, 3, and 6.

How to find the LCM:

→ List multiples of each number.

→ Find the smallest number on each list.

4: 4, 8, 12, 16, 20, 24..

3: 3, 6, 9, 12, 15, 18, 21, 24, 27....

6: 6, 12, 18, 24, 30, 36, 42...

LCM: 12

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Now, we'll Multiply by LCM:

`\sf \cfrac{3x-2}{4}* \:12-\cfrac{2x-5}{3}* \:12=\cfrac{1+x}{6}* \:12`

Simplify:

`\sf 3\left(3x-2\right)-4\left(2x-5\right)=2\left(x+1\right)`

Now, expand, Apply the Distributive property:

`\bold{ 3\left(3x-2\right)-4\left(2x-5\right)}`

`\sf 9x-6-8x+20`

Combine like terms:

`\sf x+14`

________

`\bold{ 2\left(x+1\right)}`

`\sf 2x+2`

`\sf x+14=2x+2`

Subtract 14 from both sides:

`\sf x+14-14=2x+2-14`

Simplify:

`\sf x=2x-12`

Subtract 2x from both sides:

`\sf x-2x=2x-12-2x`

Simplify:

`\sf -x=-12`

Divide both sides by -1:

`\sf \cfrac{-x}{-1}=\cfrac{-12}{-1}`

`\sf x=12`

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