Solve 2x-7/3+8x-9/14=3x-5/21

$$\frac{ 2x-7 }{ 3 } + \frac{ 8x-9 }{ 14 } = \frac{ 3x-5 }{ 21 }$$

Solve for x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 42, the least common multiple of 3,14,21.

$$14\left(2x-7\right)+3\left(8x-9\right)=2\left(3x-5\right)$$

Use the distributive property to multiply 14 by 2x-7.

$$28x-98+3\left(8x-9\right)=2\left(3x-5\right)$$

Use the distributive property to multiply 3 by 8x-9.

$$28x-98+24x-27=2\left(3x-5\right)$$

Combine 28x and 24x to get 52x.

$$52x-98-27=2\left(3x-5\right)$$

Subtract 27 from -98 to get -125.

$$52x-125=2\left(3x-5\right)$$

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

$$52x-125=6x-10$$

Subtract 6x from both sides.

$$52x-125-6x=-10$$

Combine 52x and -6x to get 46x.

$$46x-125=-10$$

Add 125 to both sides.

$$46x=-10+125$$

Add -10 and 125 to get 115.

$$46x=115$$

Divide both sides by 46.

$$x=\frac{115}{46}$$

Reduce the fraction \frac{115}{46} to lowest terms by extracting and canceling out 23.

$$x=\frac{5}{2}$$