Solve x-2/3left(-1-15/2-xright)=x/3+1

$$x- \frac{ 2 }{ 3 } \left( -1- \frac{ 15 }{ 2 } -x \right) = \frac{ x }{ 3 } +1$$

Solve for x

$$x = -\frac{7}{2} = -3\frac{1}{2} = -3.5$$

Steps for Solving Linear Equation

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

$$6x-4\left(-1-\frac{15}{2}-x\right)=2x+6$$

Convert -1 to fraction -\frac{2}{2}.

$$6x-4\left(-\frac{2}{2}-\frac{15}{2}-x\right)=2x+6$$

Since -\frac{2}{2} and \frac{15}{2} have the same denominator, subtract them by subtracting their numerators.

$$6x-4\left(\frac{-2-15}{2}-x\right)=2x+6$$

Subtract 15 from -2 to get -17.

$$6x-4\left(-\frac{17}{2}-x\right)=2x+6$$

Use the distributive property to multiply -4 by -\frac{17}{2}-x.

$$6x-4\left(-\frac{17}{2}\right)+4x=2x+6$$

Express -4\left(-\frac{17}{2}\right) as a single fraction.

$$6x+\frac{-4\left(-17\right)}{2}+4x=2x+6$$

Multiply -4 and -17 to get 68.

$$6x+\frac{68}{2}+4x=2x+6$$

Divide 68 by 2 to get 34.

$$6x+34+4x=2x+6$$

Combine 6x and 4x to get 10x.

$$10x+34=2x+6$$

Subtract 2x from both sides.

$$10x+34-2x=6$$

Combine 10x and -2x to get 8x.

$$8x+34=6$$

Subtract 34 from both sides.

$$8x=6-34$$

Subtract 34 from 6 to get -28.

$$8x=-28$$

Divide both sides by 8.

$$x=\frac{-28}{8}$$

Reduce the fraction \frac{-28}{8} to lowest terms by extracting and canceling out 4.

$$x=-\frac{7}{2}$$