Solve 3/3(x-9)+3/4(x-1)=-13

$$\frac { 3 } { 3 } ( x - 9 ) + \frac { 3 } { 4 } ( x - 1 ) = - 13$$

Solve for x

$$x = -\frac{13}{7} = -1\frac{6}{7} \approx -1.857142857$$

Steps for Solving Linear Equation

Divide 3 by 3 to get 1.

$$1\left(x-9\right)+\frac{3}{4}\left(x-1\right)=-13$$

Use the distributive property to multiply 1 by x-9.

$$x-9+\frac{3}{4}\left(x-1\right)=-13$$

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

$$x-9+\frac{3}{4}x+\frac{3}{4}\left(-1\right)=-13$$

Multiply \frac{3}{4} and -1 to get -\frac{3}{4}.

$$x-9+\frac{3}{4}x-\frac{3}{4}=-13$$

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

$$\frac{7}{4}x-9-\frac{3}{4}=-13$$

Convert -9 to fraction -\frac{36}{4}.

$$\frac{7}{4}x-\frac{36}{4}-\frac{3}{4}=-13$$

Since -\frac{36}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{4}x+\frac{-36-3}{4}=-13$$

Subtract 3 from -36 to get -39.

$$\frac{7}{4}x-\frac{39}{4}=-13$$

Add \frac{39}{4} to both sides.

$$\frac{7}{4}x=-13+\frac{39}{4}$$

Convert -13 to fraction -\frac{52}{4}.

$$\frac{7}{4}x=-\frac{52}{4}+\frac{39}{4}$$

Since -\frac{52}{4} and \frac{39}{4} have the same denominator, add them by adding their numerators.

$$\frac{7}{4}x=\frac{-52+39}{4}$$

Add -52 and 39 to get -13.

$$\frac{7}{4}x=-\frac{13}{4}$$

Multiply both sides by \frac{4}{7}, the reciprocal of \frac{7}{4}.

$$x=-\frac{13}{4}\times \frac{4}{7}$$

Multiply -\frac{13}{4} times \frac{4}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-13\times 4}{4\times 7}$$

Cancel out 4 in both numerator and denominator.

$$x=\frac{-13}{7}$$

Fraction \frac{-13}{7} can be rewritten as -\frac{13}{7} by extracting the negative sign.

$$x=-\frac{13}{7}$$