Solve pi*4x+1/180*6*(x+5)=3/4

$$\pi \cdot 4 x + \frac { 1 } { 180 } \cdot 6 \cdot ( x + 5 ) = \frac { 3 } { 4 }$$

Solve for x

$$x=\frac{35}{2\left(120\pi +1\right)}\approx 0.046297384$$

Steps for Solving Linear Equation

Multiply \frac{1}{180} and 6 to get \frac{6}{180}.

$$\pi \times 4x+\frac{6}{180}\left(x+5\right)=\frac{3}{4}$$

Reduce the fraction \frac{6}{180} to lowest terms by extracting and canceling out 6.

$$\pi \times 4x+\frac{1}{30}\left(x+5\right)=\frac{3}{4}$$

Use the distributive property to multiply \frac{1}{30} by x+5.

$$\pi \times 4x+\frac{1}{30}x+\frac{1}{30}\times 5=\frac{3}{4}$$

Multiply \frac{1}{30} and 5 to get \frac{5}{30}.

$$\pi \times 4x+\frac{1}{30}x+\frac{5}{30}=\frac{3}{4}$$

Reduce the fraction \frac{5}{30} to lowest terms by extracting and canceling out 5.

$$\pi \times 4x+\frac{1}{30}x+\frac{1}{6}=\frac{3}{4}$$

Subtract \frac{1}{6} from both sides.

$$\pi \times 4x+\frac{1}{30}x=\frac{3}{4}-\frac{1}{6}$$

Least common multiple of 4 and 6 is 12. Convert \frac{3}{4} and \frac{1}{6} to fractions with denominator 12.

$$\pi \times 4x+\frac{1}{30}x=\frac{9}{12}-\frac{2}{12}$$

Since \frac{9}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\pi \times 4x+\frac{1}{30}x=\frac{9-2}{12}$$

Subtract 2 from 9 to get 7.

$$\pi \times 4x+\frac{1}{30}x=\frac{7}{12}$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 4\pi +\frac{1}{30}.

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

Dividing by 4\pi +\frac{1}{30} undoes the multiplication by 4\pi +\frac{1}{30}.

$$x=\frac{\frac{7}{12}}{4\pi +\frac{1}{30}}$$

Divide \frac{7}{12} by 4\pi +\frac{1}{30}.

$$x=\frac{35}{2\left(120\pi +1\right)}$$