Solve the equation for x: (3x−5)/2=(2(x−1))/3+4/1

To solve any linear equation, do the following STRATEGY:

Eliminate Fractions: by Multiply both sides of the equation by the lowest common denominator (LCD).

Remove Parenthesis: by Brackets are multiplied away.

Collect x Terms: Move all x terms to one side and all other terms to other side.

Combine Like Terms: Always simplify.

Remove Coefficient of x: Divide both sides by coefficient.

Check Answer: Be sure to substitute the answer back into the original equation.

Solution:

1) flind the LCD by multiplying all the denominators, so LCD = 2 x 3 x 1 =6
2) multipy the entire equation (both sides of the equation) by the LCD you found as shown below.

[(3x−5)/2=(2(x−1))/3+4/1]6

Simplify,

6* [(3x−5)/2]=6*[(2(x−1))/3+4/1]

3 * (3x−5)=2 *(2(x−1))+4*6

3(3x - 5) = 4(x - 1) + 6(4)
9x – 15 = 4x - 4 + 24
9x – 4x = 24 - 4 + 15
      
      5x = 35
          
       x = 7

CHECK:

(3(7)−5)/2=(2(7−1))/3+4/1

21-5/2 = 2(6)/3 + 4

16/2 = 12/3 + 4

8 = 4+ 4
8 = 8 (checks ✔)