Solve -6/10x+2/5=x-1/3+1

$$- \frac{ 6 }{ 10 } x+ \frac{ 2 }{ 5 } = \frac{ x-1 }{ 3 } +1$$

Solve for x

$$x=-\frac{2}{7}\approx -0.285714286$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 10,5,3.

$$30\left(-\frac{6}{10}\right)x+12=10\left(x-1\right)+30$$

Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$30\left(-\frac{3}{5}\right)x+12=10\left(x-1\right)+30$$

Express 30\left(-\frac{3}{5}\right) as a single fraction.

$$\frac{30\left(-3\right)}{5}x+12=10\left(x-1\right)+30$$

Multiply 30 and -3 to get -90.

$$\frac{-90}{5}x+12=10\left(x-1\right)+30$$

Divide -90 by 5 to get -18.

$$-18x+12=10\left(x-1\right)+30$$

Use the distributive property to multiply 10 by x-1.

$$-18x+12=10x-10+30$$

Add -10 and 30 to get 20.

$$-18x+12=10x+20$$

Subtract 10x from both sides.

$$-18x+12-10x=20$$

Combine -18x and -10x to get -28x.

$$-28x+12=20$$

Subtract 12 from both sides.

$$-28x=20-12$$

Subtract 12 from 20 to get 8.

$$-28x=8$$

Divide both sides by -28.

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

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

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