Solve 7x-2-6/5=2x-x+1/3

$$\frac { 7 x - 2 - 6 } { 5 } = 2 x - \frac { x + 1 } { 3 }$$

Solve for x

$$x = -\frac{19}{4} = -4\frac{3}{4} = -4.75$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 5,3.

$$3\left(7x-2-6\right)=30x-5\left(x+1\right)$$

Subtract 6 from -2 to get -8.

$$3\left(7x-8\right)=30x-5\left(x+1\right)$$

Use the distributive property to multiply 3 by 7x-8.

$$21x-24=30x-5\left(x+1\right)$$

Use the distributive property to multiply -5 by x+1.

$$21x-24=30x-5x-5$$

Combine 30x and -5x to get 25x.

$$21x-24=25x-5$$

Subtract 25x from both sides.

$$21x-24-25x=-5$$

Combine 21x and -25x to get -4x.

$$-4x-24=-5$$

Add 24 to both sides.

$$-4x=-5+24$$

Add -5 and 24 to get 19.

$$-4x=19$$

Divide both sides by -4.

$$x=\frac{19}{-4}$$

Fraction \frac{19}{-4} can be rewritten as -\frac{19}{4} by extracting the negative sign.

$$x=-\frac{19}{4}$$