Solve 1/6x+1=5/18x-1/9

$$\frac{ 1 }{ 6 } x+1= \frac{ 5 }{ 18 } x- \frac{ 1 }{ 9 }$$

Solve for x

$$x=10$$

Steps for Solving Linear Equation

Subtract \frac{5}{18}x from both sides.

$$\frac{1}{6}x+1-\frac{5}{18}x=-\frac{1}{9}$$

Combine \frac{1}{6}x and -\frac{5}{18}x to get -\frac{1}{9}x.

$$-\frac{1}{9}x+1=-\frac{1}{9}$$

Subtract 1 from both sides.

$$-\frac{1}{9}x=-\frac{1}{9}-1$$

Convert 1 to fraction \frac{9}{9}.

$$-\frac{1}{9}x=-\frac{1}{9}-\frac{9}{9}$$

Since -\frac{1}{9} and \frac{9}{9} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{9}x=\frac{-1-9}{9}$$

Subtract 9 from -1 to get -10.

$$-\frac{1}{9}x=-\frac{10}{9}$$

Multiply both sides by -9, the reciprocal of -\frac{1}{9}.

$$x=-\frac{10}{9}\left(-9\right)$$

Express -\frac{10}{9}\left(-9\right) as a single fraction.

$$x=\frac{-10\left(-9\right)}{9}$$

Multiply -10 and -9 to get 90.

$$x=\frac{90}{9}$$

Divide 90 by 9 to get 10.

$$x=10$$