Solve 7/10-9x-2/4=11/5x-5/8-frac{37}{4}x+frac{1}{40}

$$\frac { 7 } { 10 } - \frac { 9 x - 2 } { 4 } = \frac { 11 } { 5 } x - \frac { 5 } { 8 } - \frac { 37 } { 4 } x + \frac { 1 } { 40 }$$

Solve for x

$$x=-\frac{3}{8}=-0.375$$

Steps for Solving Linear Equation

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

$$28-10\left(9x-2\right)=88x-25-370x+1$$

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

$$28-90x+20=88x-25-370x+1$$

Add 28 and 20 to get 48.

$$48-90x=88x-25-370x+1$$

Combine 88x and -370x to get -282x.

$$48-90x=-282x-25+1$$

Add -25 and 1 to get -24.

$$48-90x=-282x-24$$

Add 282x to both sides.

$$48-90x+282x=-24$$

Combine -90x and 282x to get 192x.

$$48+192x=-24$$

Subtract 48 from both sides.

$$192x=-24-48$$

Subtract 48 from -24 to get -72.

$$192x=-72$$

Divide both sides by 192.

$$x=\frac{-72}{192}$$

Reduce the fraction \frac{-72}{192} to lowest terms by extracting and canceling out 24.

$$x=-\frac{3}{8}$$