Solve 1/4(x-3)+1/6(2x-3)=4

$$\frac { 1 } { 4 } ( x - 3 ) + \frac { 1 } { 6 } ( 2 x - 3 ) = 4$$

Solve for x

$$x=9$$

Steps for Solving Linear Equation

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

$$\frac{1}{4}x+\frac{1}{4}\left(-3\right)+\frac{1}{6}\left(2x-3\right)=4$$

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

$$\frac{1}{4}x+\frac{-3}{4}+\frac{1}{6}\left(2x-3\right)=4$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$\frac{1}{4}x-\frac{3}{4}+\frac{1}{6}\left(2x-3\right)=4$$

Use the distributive property to multiply \frac{1}{6} by 2x-3.

$$\frac{1}{4}x-\frac{3}{4}+\frac{1}{6}\times 2x+\frac{1}{6}\left(-3\right)=4$$

Multiply \frac{1}{6} and 2 to get \frac{2}{6}.

$$\frac{1}{4}x-\frac{3}{4}+\frac{2}{6}x+\frac{1}{6}\left(-3\right)=4$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{1}{4}x-\frac{3}{4}+\frac{1}{3}x+\frac{1}{6}\left(-3\right)=4$$

Multiply \frac{1}{6} and -3 to get \frac{-3}{6}.

$$\frac{1}{4}x-\frac{3}{4}+\frac{1}{3}x+\frac{-3}{6}=4$$

Reduce the fraction \frac{-3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{4}x-\frac{3}{4}+\frac{1}{3}x-\frac{1}{2}=4$$

Combine \frac{1}{4}x and \frac{1}{3}x to get \frac{7}{12}x.

$$\frac{7}{12}x-\frac{3}{4}-\frac{1}{2}=4$$

Least common multiple of 4 and 2 is 4. Convert -\frac{3}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{7}{12}x-\frac{3}{4}-\frac{2}{4}=4$$

Since -\frac{3}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{12}x+\frac{-3-2}{4}=4$$

Subtract 2 from -3 to get -5.

$$\frac{7}{12}x-\frac{5}{4}=4$$

Add \frac{5}{4} to both sides.

$$\frac{7}{12}x=4+\frac{5}{4}$$

Convert 4 to fraction \frac{16}{4}.

$$\frac{7}{12}x=\frac{16}{4}+\frac{5}{4}$$

Since \frac{16}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

$$\frac{7}{12}x=\frac{16+5}{4}$$

Add 16 and 5 to get 21.

$$\frac{7}{12}x=\frac{21}{4}$$

Multiply both sides by \frac{12}{7}, the reciprocal of \frac{7}{12}.

$$x=\frac{21}{4}\times \frac{12}{7}$$

Multiply \frac{21}{4} times \frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{21\times 12}{4\times 7}$$

Do the multiplications in the fraction \frac{21\times 12}{4\times 7}.

$$x=\frac{252}{28}$$

Divide 252 by 28 to get 9.

$$x=9$$