Solve 1/4x+1/5=9/8(5x+11)

$$\frac { 1 } { 4 } x + \frac { 1 } { 5 } = \frac { 9 } { 8 } ( 5 x + 11 )$$

Solve for x

$$x = -\frac{487}{215} = -2\frac{57}{215} \approx -2.265116279$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{9}{8} by 5x+11.

$$\frac{1}{4}x+\frac{1}{5}=\frac{9}{8}\times 5x+\frac{9}{8}\times 11$$

Express \frac{9}{8}\times 5 as a single fraction.

$$\frac{1}{4}x+\frac{1}{5}=\frac{9\times 5}{8}x+\frac{9}{8}\times 11$$

Multiply 9 and 5 to get 45.

$$\frac{1}{4}x+\frac{1}{5}=\frac{45}{8}x+\frac{9}{8}\times 11$$

Express \frac{9}{8}\times 11 as a single fraction.

$$\frac{1}{4}x+\frac{1}{5}=\frac{45}{8}x+\frac{9\times 11}{8}$$

Multiply 9 and 11 to get 99.

$$\frac{1}{4}x+\frac{1}{5}=\frac{45}{8}x+\frac{99}{8}$$

Subtract \frac{45}{8}x from both sides.

$$\frac{1}{4}x+\frac{1}{5}-\frac{45}{8}x=\frac{99}{8}$$

Combine \frac{1}{4}x and -\frac{45}{8}x to get -\frac{43}{8}x.

$$-\frac{43}{8}x+\frac{1}{5}=\frac{99}{8}$$

Subtract \frac{1}{5} from both sides.

$$-\frac{43}{8}x=\frac{99}{8}-\frac{1}{5}$$

Least common multiple of 8 and 5 is 40. Convert \frac{99}{8} and \frac{1}{5} to fractions with denominator 40.

$$-\frac{43}{8}x=\frac{495}{40}-\frac{8}{40}$$

Since \frac{495}{40} and \frac{8}{40} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{43}{8}x=\frac{495-8}{40}$$

Subtract 8 from 495 to get 487.

$$-\frac{43}{8}x=\frac{487}{40}$$

Multiply both sides by -\frac{8}{43}, the reciprocal of -\frac{43}{8}.

$$x=\frac{487}{40}\left(-\frac{8}{43}\right)$$

Multiply \frac{487}{40} times -\frac{8}{43} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{487\left(-8\right)}{40\times 43}$$

Do the multiplications in the fraction \frac{487\left(-8\right)}{40\times 43}.

$$x=\frac{-3896}{1720}$$

Reduce the fraction \frac{-3896}{1720} to lowest terms by extracting and canceling out 8.

$$x=-\frac{487}{215}$$