Solve 49=x+x-3+18/13(x-3)

$$49 = x + x - 3 + \frac { 18 } { 13 } ( x - 3 )$$

Solve for x

$$x = \frac{365}{22} = 16\frac{13}{22} \approx 16.590909091$$

Steps for Solving Linear Equation

Combine x and x to get 2x.

$$49=2x-3+\frac{18}{13}\left(x-3\right)$$

Use the distributive property to multiply \frac{18}{13} by x-3.

$$49=2x-3+\frac{18}{13}x+\frac{18}{13}\left(-3\right)$$

Express \frac{18}{13}\left(-3\right) as a single fraction.

$$49=2x-3+\frac{18}{13}x+\frac{18\left(-3\right)}{13}$$

Multiply 18 and -3 to get -54.

$$49=2x-3+\frac{18}{13}x+\frac{-54}{13}$$

Fraction \frac{-54}{13} can be rewritten as -\frac{54}{13} by extracting the negative sign.

$$49=2x-3+\frac{18}{13}x-\frac{54}{13}$$

Combine 2x and \frac{18}{13}x to get \frac{44}{13}x.

$$49=\frac{44}{13}x-3-\frac{54}{13}$$

Convert -3 to fraction -\frac{39}{13}.

$$49=\frac{44}{13}x-\frac{39}{13}-\frac{54}{13}$$

Since -\frac{39}{13} and \frac{54}{13} have the same denominator, subtract them by subtracting their numerators.

$$49=\frac{44}{13}x+\frac{-39-54}{13}$$

Subtract 54 from -39 to get -93.

$$49=\frac{44}{13}x-\frac{93}{13}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{44}{13}x-\frac{93}{13}=49$$

Add \frac{93}{13} to both sides.

$$\frac{44}{13}x=49+\frac{93}{13}$$

Convert 49 to fraction \frac{637}{13}.

$$\frac{44}{13}x=\frac{637}{13}+\frac{93}{13}$$

Since \frac{637}{13} and \frac{93}{13} have the same denominator, add them by adding their numerators.

$$\frac{44}{13}x=\frac{637+93}{13}$$

Add 637 and 93 to get 730.

$$\frac{44}{13}x=\frac{730}{13}$$

Multiply both sides by \frac{13}{44}, the reciprocal of \frac{44}{13}.

$$x=\frac{730}{13}\times \frac{13}{44}$$

Multiply \frac{730}{13} times \frac{13}{44} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{730\times 13}{13\times 44}$$

Cancel out 13 in both numerator and denominator.

$$x=\frac{730}{44}$$

Reduce the fraction \frac{730}{44} to lowest terms by extracting and canceling out 2.

$$x=\frac{365}{22}$$