Solve 7/4(x-1)-8/9(2x-1)=-5/6

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

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

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

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

Multiply \frac{7}{4} and -1 to get -\frac{7}{4}.

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

Use the distributive property to multiply -\frac{8}{9} by 2x-1.

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

Express -\frac{8}{9}\times 2 as a single fraction.

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

Multiply -8 and 2 to get -16.

$$\frac{7}{4}x-\frac{7}{4}+\frac{-16}{9}x-\frac{8}{9}\left(-1\right)=-\frac{5}{6}$$

Fraction \frac{-16}{9} can be rewritten as -\frac{16}{9} by extracting the negative sign.

$$\frac{7}{4}x-\frac{7}{4}-\frac{16}{9}x-\frac{8}{9}\left(-1\right)=-\frac{5}{6}$$

Multiply -\frac{8}{9} and -1 to get \frac{8}{9}.

$$\frac{7}{4}x-\frac{7}{4}-\frac{16}{9}x+\frac{8}{9}=-\frac{5}{6}$$

Combine \frac{7}{4}x and -\frac{16}{9}x to get -\frac{1}{36}x.

$$-\frac{1}{36}x-\frac{7}{4}+\frac{8}{9}=-\frac{5}{6}$$

Least common multiple of 4 and 9 is 36. Convert -\frac{7}{4} and \frac{8}{9} to fractions with denominator 36.

$$-\frac{1}{36}x-\frac{63}{36}+\frac{32}{36}=-\frac{5}{6}$$

Since -\frac{63}{36} and \frac{32}{36} have the same denominator, add them by adding their numerators.

$$-\frac{1}{36}x+\frac{-63+32}{36}=-\frac{5}{6}$$

Add -63 and 32 to get -31.

$$-\frac{1}{36}x-\frac{31}{36}=-\frac{5}{6}$$

Add \frac{31}{36} to both sides.

$$-\frac{1}{36}x=-\frac{5}{6}+\frac{31}{36}$$

Least common multiple of 6 and 36 is 36. Convert -\frac{5}{6} and \frac{31}{36} to fractions with denominator 36.

$$-\frac{1}{36}x=-\frac{30}{36}+\frac{31}{36}$$

Since -\frac{30}{36} and \frac{31}{36} have the same denominator, add them by adding their numerators.

$$-\frac{1}{36}x=\frac{-30+31}{36}$$

Add -30 and 31 to get 1.

$$-\frac{1}{36}x=\frac{1}{36}$$

Multiply both sides by -36, the reciprocal of -\frac{1}{36}.

$$x=\frac{1}{36}\left(-36\right)$$

Multiply \frac{1}{36} and -36 to get \frac{-36}{36}.

$$x=\frac{-36}{36}$$

Divide -36 by 36 to get -1.

$$x=-1$$