Solve 2/3(4x-1)-[4x-1-3x/2]=x-7/2

$$\frac { 2 } { 3 } ( 4 x - 1 ) - [ 4 x - \frac { 1 - 3 x } { 2 } ] = \frac { x - 7 } { 2 }$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$4\left(4x-1\right)-6\left(4x-\frac{1-3x}{2}\right)=3\left(x-7\right)$$

Use the distributive property to multiply 4 by 4x-1.

$$16x-4-6\left(4x-\frac{1-3x}{2}\right)=3\left(x-7\right)$$

Use the distributive property to multiply 3 by x-7.

$$16x-4-6\left(4x-\frac{1-3x}{2}\right)=3x-21$$

Divide each term of 1-3x by 2 to get \frac{1}{2}-\frac{3}{2}x.

$$16x-4-6\left(4x-\left(\frac{1}{2}-\frac{3}{2}x\right)\right)=3x-21$$

To find the opposite of \frac{1}{2}-\frac{3}{2}x, find the opposite of each term.

$$16x-4-6\left(4x-\frac{1}{2}-\left(-\frac{3}{2}x\right)\right)=3x-21$$

The opposite of -\frac{3}{2}x is \frac{3}{2}x.

$$16x-4-6\left(4x-\frac{1}{2}+\frac{3}{2}x\right)=3x-21$$

Combine 4x and \frac{3}{2}x to get \frac{11}{2}x.

$$16x-4-6\left(\frac{11}{2}x-\frac{1}{2}\right)=3x-21$$

Use the distributive property to multiply -6 by \frac{11}{2}x-\frac{1}{2}.

$$16x-4-6\times \frac{11}{2}x-6\left(-\frac{1}{2}\right)=3x-21$$

Express -6\times \frac{11}{2} as a single fraction.

$$16x-4+\frac{-6\times 11}{2}x-6\left(-\frac{1}{2}\right)=3x-21$$

Multiply -6 and 11 to get -66.

$$16x-4+\frac{-66}{2}x-6\left(-\frac{1}{2}\right)=3x-21$$

Divide -66 by 2 to get -33.

$$16x-4-33x-6\left(-\frac{1}{2}\right)=3x-21$$

Express -6\left(-\frac{1}{2}\right) as a single fraction.

$$16x-4-33x+\frac{-6\left(-1\right)}{2}=3x-21$$

Multiply -6 and -1 to get 6.

$$16x-4-33x+\frac{6}{2}=3x-21$$

Divide 6 by 2 to get 3.

$$16x-4-33x+3=3x-21$$

Combine 16x and -33x to get -17x.

$$-17x-4+3=3x-21$$

Add -4 and 3 to get -1.

$$-17x-1=3x-21$$

Subtract 3x from both sides.

$$-17x-1-3x=-21$$

Combine -17x and -3x to get -20x.

$$-20x-1=-21$$

Add 1 to both sides.

$$-20x=-21+1$$

Add -21 and 1 to get -20.

$$-20x=-20$$

Divide both sides by -20.

$$x=\frac{-20}{-20}$$

Divide -20 by -20 to get 1.

$$x=1$$