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
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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]
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[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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