Solve 1/4(2x-5)=1/3(15-2x)-15/12

$$\frac{ 1 }{ 4 } (2x-5)= \frac{ 1 }{ 3 } (15-2x)- \frac{ 15 }{ 12 }$$

Solve for x

$$x = \frac{30}{7} = 4\frac{2}{7} \approx 4.285714286$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{4} by 2x-5.

$$\frac{1}{4}\times 2x+\frac{1}{4}\left(-5\right)=\frac{1}{3}\left(15-2x\right)-\frac{15}{12}$$

Multiply \frac{1}{4} and 2 to get \frac{2}{4}.

$$\frac{2}{4}x+\frac{1}{4}\left(-5\right)=\frac{1}{3}\left(15-2x\right)-\frac{15}{12}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}x+\frac{1}{4}\left(-5\right)=\frac{1}{3}\left(15-2x\right)-\frac{15}{12}$$

Multiply \frac{1}{4} and -5 to get \frac{-5}{4}.

$$\frac{1}{2}x+\frac{-5}{4}=\frac{1}{3}\left(15-2x\right)-\frac{15}{12}$$

Fraction \frac{-5}{4} can be rewritten as -\frac{5}{4} by extracting the negative sign.

$$\frac{1}{2}x-\frac{5}{4}=\frac{1}{3}\left(15-2x\right)-\frac{15}{12}$$

Use the distributive property to multiply \frac{1}{3} by 15-2x.

$$\frac{1}{2}x-\frac{5}{4}=\frac{1}{3}\times 15+\frac{1}{3}\left(-2\right)x-\frac{15}{12}$$

Multiply \frac{1}{3} and 15 to get \frac{15}{3}.

$$\frac{1}{2}x-\frac{5}{4}=\frac{15}{3}+\frac{1}{3}\left(-2\right)x-\frac{15}{12}$$

Divide 15 by 3 to get 5.

$$\frac{1}{2}x-\frac{5}{4}=5+\frac{1}{3}\left(-2\right)x-\frac{15}{12}$$

Multiply \frac{1}{3} and -2 to get \frac{-2}{3}.

$$\frac{1}{2}x-\frac{5}{4}=5+\frac{-2}{3}x-\frac{15}{12}$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$\frac{1}{2}x-\frac{5}{4}=5-\frac{2}{3}x-\frac{15}{12}$$

Reduce the fraction \frac{15}{12} to lowest terms by extracting and canceling out 3.

$$\frac{1}{2}x-\frac{5}{4}=5-\frac{2}{3}x-\frac{5}{4}$$

Convert 5 to fraction \frac{20}{4}.

$$\frac{1}{2}x-\frac{5}{4}=\frac{20}{4}-\frac{2}{3}x-\frac{5}{4}$$

Since \frac{20}{4} and \frac{5}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}x-\frac{5}{4}=\frac{20-5}{4}-\frac{2}{3}x$$

Subtract 5 from 20 to get 15.

$$\frac{1}{2}x-\frac{5}{4}=\frac{15}{4}-\frac{2}{3}x$$

Add \frac{2}{3}x to both sides.

$$\frac{1}{2}x-\frac{5}{4}+\frac{2}{3}x=\frac{15}{4}$$

Combine \frac{1}{2}x and \frac{2}{3}x to get \frac{7}{6}x.

$$\frac{7}{6}x-\frac{5}{4}=\frac{15}{4}$$

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

$$\frac{7}{6}x=\frac{15}{4}+\frac{5}{4}$$

Since \frac{15}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

$$\frac{7}{6}x=\frac{15+5}{4}$$

Add 15 and 5 to get 20.

$$\frac{7}{6}x=\frac{20}{4}$$

Divide 20 by 4 to get 5.

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

Multiply both sides by \frac{6}{7}, the reciprocal of \frac{7}{6}.

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

Express 5\times \frac{6}{7} as a single fraction.

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

Multiply 5 and 6 to get 30.

$$x=\frac{30}{7}$$