Solve (7/12+11/30x)div71/4=1/3

$$( \frac{ 7 }{ 12 } + \frac{ 11 }{ 30 } x) \div 7 \frac { 1 } { 4 } = \frac{ 1 }{ 3 }$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Divide \frac{7}{12}+\frac{11}{30}x by \frac{7\times 4+1}{4} by multiplying \frac{7}{12}+\frac{11}{30}x by the reciprocal of \frac{7\times 4+1}{4}.

$$\frac{\left(\frac{7}{12}+\frac{11}{30}x\right)\times 4}{7\times 4+1}=\frac{1}{3}$$

Multiply 7 and 4 to get 28.

$$\frac{\left(\frac{7}{12}+\frac{11}{30}x\right)\times 4}{28+1}=\frac{1}{3}$$

Add 28 and 1 to get 29.

$$\frac{\left(\frac{7}{12}+\frac{11}{30}x\right)\times 4}{29}=\frac{1}{3}$$

Use the distributive property to multiply \frac{7}{12}+\frac{11}{30}x by 4.

$$\frac{\frac{7}{12}\times 4+\frac{11}{30}x\times 4}{29}=\frac{1}{3}$$

Express \frac{7}{12}\times 4 as a single fraction.

$$\frac{\frac{7\times 4}{12}+\frac{11}{30}x\times 4}{29}=\frac{1}{3}$$

Multiply 7 and 4 to get 28.

$$\frac{\frac{28}{12}+\frac{11}{30}x\times 4}{29}=\frac{1}{3}$$

Reduce the fraction \frac{28}{12} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{7}{3}+\frac{11}{30}x\times 4}{29}=\frac{1}{3}$$

Express \frac{11}{30}\times 4 as a single fraction.

$$\frac{\frac{7}{3}+\frac{11\times 4}{30}x}{29}=\frac{1}{3}$$

Multiply 11 and 4 to get 44.

$$\frac{\frac{7}{3}+\frac{44}{30}x}{29}=\frac{1}{3}$$

Reduce the fraction \frac{44}{30} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{7}{3}+\frac{22}{15}x}{29}=\frac{1}{3}$$

Divide each term of \frac{7}{3}+\frac{22}{15}x by 29 to get \frac{7}{87}+\frac{22}{435}x.

$$\frac{7}{87}+\frac{22}{435}x=\frac{1}{3}$$

Subtract \frac{7}{87} from both sides.

$$\frac{22}{435}x=\frac{1}{3}-\frac{7}{87}$$

Least common multiple of 3 and 87 is 87. Convert \frac{1}{3} and \frac{7}{87} to fractions with denominator 87.

$$\frac{22}{435}x=\frac{29}{87}-\frac{7}{87}$$

Since \frac{29}{87} and \frac{7}{87} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22}{435}x=\frac{29-7}{87}$$

Subtract 7 from 29 to get 22.

$$\frac{22}{435}x=\frac{22}{87}$$

Multiply both sides by \frac{435}{22}, the reciprocal of \frac{22}{435}.

$$x=\frac{22}{87}\times \frac{435}{22}$$

Multiply \frac{22}{87} times \frac{435}{22} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{22\times 435}{87\times 22}$$

Cancel out 22 in both numerator and denominator.

$$x=\frac{435}{87}$$

Divide 435 by 87 to get 5.

$$x=5$$