Solve x-1/2-5x-3/3=3

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

Solve for x

$$x = -\frac{15}{7} = -2\frac{1}{7} \approx -2.142857143$$

Steps for Solving Linear Equation

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

$$3\left(x-1\right)-2\left(5x-3\right)=18$$

Use the distributive property to multiply 3 by x-1.

$$3x-3-2\left(5x-3\right)=18$$

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

$$3x-3-10x+6=18$$

Combine 3x and -10x to get -7x.

$$-7x-3+6=18$$

Add -3 and 6 to get 3.

$$-7x+3=18$$

Subtract 3 from both sides.

$$-7x=18-3$$

Subtract 3 from 18 to get 15.

$$-7x=15$$

Divide both sides by -7.

$$x=\frac{15}{-7}$$

Fraction \frac{15}{-7} can be rewritten as -\frac{15}{7} by extracting the negative sign.

$$x=-\frac{15}{7}$$