Solve 7/10-9x-2/4=18/5x-5/8-frac{37}{4}+frac{1}{40}

$$\frac { 7 } { 10 } - \frac { 9 x - 2 } { 4 } = \frac { 18 } { 5 } x - \frac { 5 } { 8 } - \frac { 37 } { 4 } + \frac { 1 } { 40 }$$

Solve for x

$$x = \frac{17}{9} = 1\frac{8}{9} \approx 1.888888889$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 40, the least common multiple of 10,4,5,8,40.

$$28-10\left(9x-2\right)=144x-25-370+1$$

Use the distributive property to multiply -10 by 9x-2.

$$28-90x+20=144x-25-370+1$$

Add 28 and 20 to get 48.

$$48-90x=144x-25-370+1$$

Subtract 370 from -25 to get -395.

$$48-90x=144x-395+1$$

Add -395 and 1 to get -394.

$$48-90x=144x-394$$

Subtract 144x from both sides.

$$48-90x-144x=-394$$

Combine -90x and -144x to get -234x.

$$48-234x=-394$$

Subtract 48 from both sides.

$$-234x=-394-48$$

Subtract 48 from -394 to get -442.

$$-234x=-442$$

Divide both sides by -234.

$$x=\frac{-442}{-234}$$

Reduce the fraction \frac{-442}{-234} to lowest terms by extracting and canceling out -26.

$$x=\frac{17}{9}$$