Solve 9/8x-17/6(-5/4x-1)=2x+1/3(frac{7}{4}x+frac{11}{4})

$$\frac{ 9 }{ 8 } x- \frac{ 17 }{ 6 } ( \frac{ -5 }{ 4 } x-1)=2x+ \frac{ 1 }{ 3 } ( \frac{ 7 }{ 4 } x+ \frac{ 11 }{ 4 } )$$

Solve for x

$$x=-\frac{23}{25}=-0.92$$

Steps for Solving Linear Equation

Fraction \frac{-5}{4} can be rewritten as -\frac{5}{4} by extracting the negative sign.

$$\frac{9}{8}x-\frac{17}{6}\left(-\frac{5}{4}x-1\right)=2x+\frac{1}{3}\left(\frac{7}{4}x+\frac{11}{4}\right)$$

Use the distributive property to multiply -\frac{17}{6} by -\frac{5}{4}x-1.

$$\frac{9}{8}x-\frac{17}{6}\left(-\frac{5}{4}\right)x-\frac{17}{6}\left(-1\right)=2x+\frac{1}{3}\left(\frac{7}{4}x+\frac{11}{4}\right)$$

Multiply -\frac{17}{6} times -\frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9}{8}x+\frac{-17\left(-5\right)}{6\times 4}x-\frac{17}{6}\left(-1\right)=2x+\frac{1}{3}\left(\frac{7}{4}x+\frac{11}{4}\right)$$

Do the multiplications in the fraction \frac{-17\left(-5\right)}{6\times 4}.

$$\frac{9}{8}x+\frac{85}{24}x-\frac{17}{6}\left(-1\right)=2x+\frac{1}{3}\left(\frac{7}{4}x+\frac{11}{4}\right)$$

Multiply -\frac{17}{6} and -1 to get \frac{17}{6}.

$$\frac{9}{8}x+\frac{85}{24}x+\frac{17}{6}=2x+\frac{1}{3}\left(\frac{7}{4}x+\frac{11}{4}\right)$$

Combine \frac{9}{8}x and \frac{85}{24}x to get \frac{14}{3}x.

$$\frac{14}{3}x+\frac{17}{6}=2x+\frac{1}{3}\left(\frac{7}{4}x+\frac{11}{4}\right)$$

Use the distributive property to multiply \frac{1}{3} by \frac{7}{4}x+\frac{11}{4}.

$$\frac{14}{3}x+\frac{17}{6}=2x+\frac{1}{3}\times \frac{7}{4}x+\frac{1}{3}\times \frac{11}{4}$$

Multiply \frac{1}{3} times \frac{7}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{14}{3}x+\frac{17}{6}=2x+\frac{1\times 7}{3\times 4}x+\frac{1}{3}\times \frac{11}{4}$$

Do the multiplications in the fraction \frac{1\times 7}{3\times 4}.

$$\frac{14}{3}x+\frac{17}{6}=2x+\frac{7}{12}x+\frac{1}{3}\times \frac{11}{4}$$

Multiply \frac{1}{3} times \frac{11}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{14}{3}x+\frac{17}{6}=2x+\frac{7}{12}x+\frac{1\times 11}{3\times 4}$$

Do the multiplications in the fraction \frac{1\times 11}{3\times 4}.

$$\frac{14}{3}x+\frac{17}{6}=2x+\frac{7}{12}x+\frac{11}{12}$$

Combine 2x and \frac{7}{12}x to get \frac{31}{12}x.

$$\frac{14}{3}x+\frac{17}{6}=\frac{31}{12}x+\frac{11}{12}$$

Subtract \frac{31}{12}x from both sides.

$$\frac{14}{3}x+\frac{17}{6}-\frac{31}{12}x=\frac{11}{12}$$

Combine \frac{14}{3}x and -\frac{31}{12}x to get \frac{25}{12}x.

$$\frac{25}{12}x+\frac{17}{6}=\frac{11}{12}$$

Subtract \frac{17}{6} from both sides.

$$\frac{25}{12}x=\frac{11}{12}-\frac{17}{6}$$

Least common multiple of 12 and 6 is 12. Convert \frac{11}{12} and \frac{17}{6} to fractions with denominator 12.

$$\frac{25}{12}x=\frac{11}{12}-\frac{34}{12}$$

Since \frac{11}{12} and \frac{34}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25}{12}x=\frac{11-34}{12}$$

Subtract 34 from 11 to get -23.

$$\frac{25}{12}x=-\frac{23}{12}$$

Multiply both sides by \frac{12}{25}, the reciprocal of \frac{25}{12}.

$$x=-\frac{23}{12}\times \frac{12}{25}$$

Multiply -\frac{23}{12} times \frac{12}{25} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-23\times 12}{12\times 25}$$

Cancel out 12 in both numerator and denominator.

$$x=\frac{-23}{25}$$

Fraction \frac{-23}{25} can be rewritten as -\frac{23}{25} by extracting the negative sign.

$$x=-\frac{23}{25}$$