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

Solve The Equation 3x2 4 2x 5 1 X 3 6 class=

Sagot :

Answer:

  • [tex]\boxed{\sf x=12}[/tex]

Step-by-step explanation:

[tex]\sf \cfrac{3x-2}{4}-\cfrac{2x-5}{3}=\cfrac{1+x}{6}[/tex]

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

_________

Now, we'll Multiply by LCM:

[tex]\sf \cfrac{3x-2}{4}\times \:12-\cfrac{2x-5}{3}\times \:12=\cfrac{1+x}{6}\times \:12[/tex]

Simplify:

[tex]\sf 3\left(3x-2\right)-4\left(2x-5\right)=2\left(x+1\right)[/tex]

Now, expand, Apply the Distributive property:

[tex]\bold{ 3\left(3x-2\right)-4\left(2x-5\right)}[/tex]

[tex]\sf 9x-6-8x+20[/tex]

Combine like terms:

[tex]\sf x+14[/tex]

________

[tex]\bold{ 2\left(x+1\right)}[/tex]

[tex]\sf 2x+2[/tex]

[tex]\sf x+14=2x+2[/tex]

Subtract 14 from both sides:

[tex]\sf x+14-14=2x+2-14[/tex]

Simplify:

[tex]\sf x=2x-12[/tex]

Subtract 2x from both sides:

[tex]\sf x-2x=2x-12-2x[/tex]

Simplify:

[tex]\sf -x=-12[/tex]

Divide both sides by -1:

[tex]\sf \cfrac{-x}{-1}=\cfrac{-12}{-1}[/tex]

[tex]\sf x=12[/tex]

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