Solve x+3/4+5(7x+9)/3=3(4x+3)/12-7/2

$$\frac { x + 3 } { 4 } + \frac { 5 ( 7 x + 9 ) } { 3 } = \frac { 3 ( 4 x + 3 ) } { 12 } - \frac { 7 } { 2 }$$

Solve for x

$$x = -\frac{222}{131} = -1\frac{91}{131} \approx -1.694656489$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 4,3,12,2.

$$3\left(x+3\right)+4\times 5\left(7x+9\right)=3\left(4x+3\right)-42$$

Use the distributive property to multiply 3 by x+3.

$$3x+9+4\times 5\left(7x+9\right)=3\left(4x+3\right)-42$$

Multiply 4 and 5 to get 20.

$$3x+9+20\left(7x+9\right)=3\left(4x+3\right)-42$$

Use the distributive property to multiply 20 by 7x+9.

$$3x+9+140x+180=3\left(4x+3\right)-42$$

Combine 3x and 140x to get 143x.

$$143x+9+180=3\left(4x+3\right)-42$$

Add 9 and 180 to get 189.

$$143x+189=3\left(4x+3\right)-42$$

Use the distributive property to multiply 3 by 4x+3.

$$143x+189=12x+9-42$$

Subtract 42 from 9 to get -33.

$$143x+189=12x-33$$

Subtract 12x from both sides.

$$143x+189-12x=-33$$

Combine 143x and -12x to get 131x.

$$131x+189=-33$$

Subtract 189 from both sides.

$$131x=-33-189$$

Subtract 189 from -33 to get -222.

$$131x=-222$$

Divide both sides by 131.

$$x=\frac{-222}{131}$$

Fraction \frac{-222}{131} can be rewritten as -\frac{222}{131} by extracting the negative sign.

$$x=-\frac{222}{131}$$