Solve 1/4x+1/6(x-1)=1

$$\frac { 1 } { 4 } x + \frac { 1 } { 6 } ( x - 1 ) = 1$$

Solve for x

$$x = \frac{14}{5} = 2\frac{4}{5} = 2.8$$

Steps for Solving Linear Equation

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

$$\frac{1}{4}x+\frac{1}{6}x+\frac{1}{6}\left(-1\right)=1$$

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

$$\frac{1}{4}x+\frac{1}{6}x-\frac{1}{6}=1$$

Combine \frac{1}{4}x and \frac{1}{6}x to get \frac{5}{12}x.

$$\frac{5}{12}x-\frac{1}{6}=1$$

Add \frac{1}{6} to both sides.

$$\frac{5}{12}x=1+\frac{1}{6}$$

Convert 1 to fraction \frac{6}{6}.

$$\frac{5}{12}x=\frac{6}{6}+\frac{1}{6}$$

Since \frac{6}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{5}{12}x=\frac{6+1}{6}$$

Add 6 and 1 to get 7.

$$\frac{5}{12}x=\frac{7}{6}$$

Multiply both sides by \frac{12}{5}, the reciprocal of \frac{5}{12}.

$$x=\frac{7}{6}\times \frac{12}{5}$$

Multiply \frac{7}{6} times \frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{7\times 12}{6\times 5}$$

Do the multiplications in the fraction \frac{7\times 12}{6\times 5}.

$$x=\frac{84}{30}$$

Reduce the fraction \frac{84}{30} to lowest terms by extracting and canceling out 6.

$$x=\frac{14}{5}$$