Solve x-1/5-2+3x/2+7/10=-x

$$\frac{ x-1 }{ 5 } - \frac{ 2+3x }{ 2 } + \frac{ 7 }{ 10 } =-x$$

Solve for x

$$x = -\frac{5}{3} = -1\frac{2}{3} \approx -1.666666667$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 5,2,10.

$$2\left(x-1\right)-5\left(2+3x\right)+7=-10x$$

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

$$2x-2-5\left(2+3x\right)+7=-10x$$

Use the distributive property to multiply -5 by 2+3x.

$$2x-2-10-15x+7=-10x$$

Subtract 10 from -2 to get -12.

$$2x-12-15x+7=-10x$$

Combine 2x and -15x to get -13x.

$$-13x-12+7=-10x$$

Add -12 and 7 to get -5.

$$-13x-5=-10x$$

Add 10x to both sides.

$$-13x-5+10x=0$$

Combine -13x and 10x to get -3x.

$$-3x-5=0$$

Add 5 to both sides. Anything plus zero gives itself.

$$-3x=5$$

Divide both sides by -3.

$$x=\frac{5}{-3}$$

Fraction \frac{5}{-3} can be rewritten as -\frac{5}{3} by extracting the negative sign.

$$x=-\frac{5}{3}$$