Solve (11/4+x):x=30/16:2/4

$$( \frac { 11 } { 4 } + x ) : x = \frac { 30 } { 16 } : \frac { 2 } { 4 }$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$\frac{11}{4}+x=2x\times \frac{30}{16}$$

Reduce the fraction \frac{30}{16} to lowest terms by extracting and canceling out 2.

$$\frac{11}{4}+x=2x\times \frac{15}{8}$$

Express 2\times \frac{15}{8} as a single fraction.

$$\frac{11}{4}+x=\frac{2\times 15}{8}x$$

Multiply 2 and 15 to get 30.

$$\frac{11}{4}+x=\frac{30}{8}x$$

Reduce the fraction \frac{30}{8} to lowest terms by extracting and canceling out 2.

$$\frac{11}{4}+x=\frac{15}{4}x$$

Subtract \frac{15}{4}x from both sides.

$$\frac{11}{4}+x-\frac{15}{4}x=0$$

Combine x and -\frac{15}{4}x to get -\frac{11}{4}x.

$$\frac{11}{4}-\frac{11}{4}x=0$$

Subtract \frac{11}{4} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{11}{4}x=-\frac{11}{4}$$

Multiply both sides by -\frac{4}{11}, the reciprocal of -\frac{11}{4}.

$$x=-\frac{11}{4}\left(-\frac{4}{11}\right)$$

Multiply -\frac{11}{4} times -\frac{4}{11} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-11\left(-4\right)}{4\times 11}$$

Do the multiplications in the fraction \frac{-11\left(-4\right)}{4\times 11}.

$$x=\frac{44}{44}$$

Divide 44 by 44 to get 1.

$$x=1$$