Question

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

Answer 1

Answer:

• $\boxed{\sf x=12}$

Step-by-step 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:

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

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:

$\sf x+14$

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

$\sf 2x+2$

$\sf x+14=2x+2$

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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