Solve 5x-7/12-3x+8/5=7x-3/10-8x-7/15

$$\frac { 5 x - 7 } { 12 } - \frac { 3 x + 8 } { 5 } = \frac { 7 x - 3 } { 10 } - \frac { 8 x - 7 } { 15 }$$

Solve for x

$$x = -\frac{47}{7} = -6\frac{5}{7} \approx -6.714285714$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 12,5,10,15.

$$5\left(5x-7\right)-12\left(3x+8\right)=6\left(7x-3\right)-4\left(8x-7\right)$$

Use the distributive property to multiply 5 by 5x-7.

$$25x-35-12\left(3x+8\right)=6\left(7x-3\right)-4\left(8x-7\right)$$

Use the distributive property to multiply -12 by 3x+8.

$$25x-35-36x-96=6\left(7x-3\right)-4\left(8x-7\right)$$

Combine 25x and -36x to get -11x.

$$-11x-35-96=6\left(7x-3\right)-4\left(8x-7\right)$$

Subtract 96 from -35 to get -131.

$$-11x-131=6\left(7x-3\right)-4\left(8x-7\right)$$

Use the distributive property to multiply 6 by 7x-3.

$$-11x-131=42x-18-4\left(8x-7\right)$$

Use the distributive property to multiply -4 by 8x-7.

$$-11x-131=42x-18-32x+28$$

Combine 42x and -32x to get 10x.

$$-11x-131=10x-18+28$$

Add -18 and 28 to get 10.

$$-11x-131=10x+10$$

Subtract 10x from both sides.

$$-11x-131-10x=10$$

Combine -11x and -10x to get -21x.

$$-21x-131=10$$

Add 131 to both sides.

$$-21x=10+131$$

Add 10 and 131 to get 141.

$$-21x=141$$

Divide both sides by -21.

$$x=\frac{141}{-21}$$

Reduce the fraction \frac{141}{-21} to lowest terms by extracting and canceling out 3.

$$x=-\frac{47}{7}$$