Solve 3/4x-9/10x-8=1/3x+1/4x+2

$$\frac { 3 } { 4 } x - \frac { 9 } { 10 } x - 8 = \frac { 1 } { 3 } x + \frac { 1 } { 4 } x + 2$$

Solve for x

$$x = -\frac{150}{11} = -13\frac{7}{11} \approx -13.636363636$$

Steps for Solving Linear Equation

Combine \frac{3}{4}x and -\frac{9}{10}x to get -\frac{3}{20}x.

$$-\frac{3}{20}x-8=\frac{1}{3}x+\frac{1}{4}x+2$$

Combine \frac{1}{3}x and \frac{1}{4}x to get \frac{7}{12}x.

$$-\frac{3}{20}x-8=\frac{7}{12}x+2$$

Subtract \frac{7}{12}x from both sides.

$$-\frac{3}{20}x-8-\frac{7}{12}x=2$$

Combine -\frac{3}{20}x and -\frac{7}{12}x to get -\frac{11}{15}x.

$$-\frac{11}{15}x-8=2$$

Add 8 to both sides.

$$-\frac{11}{15}x=2+8$$

Add 2 and 8 to get 10.

$$-\frac{11}{15}x=10$$

Multiply both sides by -\frac{15}{11}, the reciprocal of -\frac{11}{15}.

$$x=10\left(-\frac{15}{11}\right)$$

Express 10\left(-\frac{15}{11}\right) as a single fraction.

$$x=\frac{10\left(-15\right)}{11}$$

Multiply 10 and -15 to get -150.

$$x=\frac{-150}{11}$$

Fraction \frac{-150}{11} can be rewritten as -\frac{150}{11} by extracting the negative sign.

$$x=-\frac{150}{11}$$