Solve 3x/8-7/10-12x-5/16-2x-3/20+frac{4x+9}{4}+frac{7}{80}=0

$$\frac { 3 x } { 8 } - \frac { 7 } { 10 } - \frac { 12 x - 5 } { 16 } - \frac { 2 x - 3 } { 20 } + \frac { 4 x + 9 } { 4 } + \frac { 7 } { 80 } = 0$$

Solve for x

$$x=-4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 80, the least common multiple of 8,10,16,20,4,80.

$$10\times 3x-56-5\left(12x-5\right)-4\left(2x-3\right)+20\left(4x+9\right)+7=0$$

Multiply 10 and 3 to get 30.

$$30x-56-5\left(12x-5\right)-4\left(2x-3\right)+20\left(4x+9\right)+7=0$$

Use the distributive property to multiply -5 by 12x-5.

$$30x-56-60x+25-4\left(2x-3\right)+20\left(4x+9\right)+7=0$$

Combine 30x and -60x to get -30x.

$$-30x-56+25-4\left(2x-3\right)+20\left(4x+9\right)+7=0$$

Add -56 and 25 to get -31.

$$-30x-31-4\left(2x-3\right)+20\left(4x+9\right)+7=0$$

Use the distributive property to multiply -4 by 2x-3.

$$-30x-31-8x+12+20\left(4x+9\right)+7=0$$

Combine -30x and -8x to get -38x.

$$-38x-31+12+20\left(4x+9\right)+7=0$$

Add -31 and 12 to get -19.

$$-38x-19+20\left(4x+9\right)+7=0$$

Use the distributive property to multiply 20 by 4x+9.

$$-38x-19+80x+180+7=0$$

Combine -38x and 80x to get 42x.

$$42x-19+180+7=0$$

Add -19 and 180 to get 161.

$$42x+161+7=0$$

Add 161 and 7 to get 168.

$$42x+168=0$$

Subtract 168 from both sides. Anything subtracted from zero gives its negation.

$$42x=-168$$

Divide both sides by 42.

$$x=\frac{-168}{42}$$

Divide -168 by 42 to get -4.

$$x=-4$$