Solve 6(1/2x+1)-7=-3(-1/2x-1)

$$6 ( \frac { 1 } { 2 } x + 1 ) - 7 = - 3 ( - \frac { 1 } { 2 } x - 1 )$$

Solve for x

$$x = \frac{8}{3} = 2\frac{2}{3} \approx 2.666666667$$

Steps for Solving Linear Equation

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

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

Multiply 6 and \frac{1}{2} to get \frac{6}{2}.

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

Divide 6 by 2 to get 3.

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

Subtract 7 from 6 to get -1.

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

Use the distributive property to multiply -3 by -\frac{1}{2}x-1.

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

Express -3\left(-\frac{1}{2}\right) as a single fraction.

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

Multiply -3 and -1 to get 3.

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

Subtract \frac{3}{2}x from both sides.

$$3x-1-\frac{3}{2}x=3$$

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

$$\frac{3}{2}x-1=3$$

Add 1 to both sides.

$$\frac{3}{2}x=3+1$$

Add 3 and 1 to get 4.

$$\frac{3}{2}x=4$$

Multiply both sides by \frac{2}{3}, the reciprocal of \frac{3}{2}.

$$x=4\times \frac{2}{3}$$

Express 4\times \frac{2}{3} as a single fraction.

$$x=\frac{4\times 2}{3}$$

Multiply 4 and 2 to get 8.

$$x=\frac{8}{3}$$