Solve 3(2x+1)/4-2(2x-1)/3=1

$$\frac { 3 ( 2 x + 1 ) } { 4 } - \frac { 2 ( 2 x - 1 ) } { 3 } = 1$$

Solve for x

$$x = -\frac{5}{2} = -2\frac{1}{2} = -2.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 4,3.

$$3\times 3\left(2x+1\right)-4\times 2\left(2x-1\right)=12$$

Multiply 3 and 3 to get 9.

$$9\left(2x+1\right)-4\times 2\left(2x-1\right)=12$$

Use the distributive property to multiply 9 by 2x+1.

$$18x+9-4\times 2\left(2x-1\right)=12$$

Multiply -4 and 2 to get -8.

$$18x+9-8\left(2x-1\right)=12$$

Use the distributive property to multiply -8 by 2x-1.

$$18x+9-16x+8=12$$

Combine 18x and -16x to get 2x.

$$2x+9+8=12$$

Add 9 and 8 to get 17.

$$2x+17=12$$

Subtract 17 from both sides.

$$2x=12-17$$

Subtract 17 from 12 to get -5.

$$2x=-5$$

Divide both sides by 2.

$$x=\frac{-5}{2}$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$x=-\frac{5}{2}$$