Solve 1/100*4x+1/160*6*(x+5)=3/4

$$\frac { 1 } { 100 } \cdot 4 x + \frac { 1 } { 160 } \cdot 6 \cdot ( x + 5 ) = \frac { 3 } { 4 }$$

Solve for x

$$x = \frac{225}{31} = 7\frac{8}{31} \approx 7.258064516$$

Steps for Solving Linear Equation

Multiply \frac{1}{100} and 4 to get \frac{4}{100}.

$$\frac{4}{100}x+\frac{1}{160}\times 6\left(x+5\right)=\frac{3}{4}$$

Reduce the fraction \frac{4}{100} to lowest terms by extracting and canceling out 4.

$$\frac{1}{25}x+\frac{1}{160}\times 6\left(x+5\right)=\frac{3}{4}$$

Multiply \frac{1}{160} and 6 to get \frac{6}{160}.

$$\frac{1}{25}x+\frac{6}{160}\left(x+5\right)=\frac{3}{4}$$

Reduce the fraction \frac{6}{160} to lowest terms by extracting and canceling out 2.

$$\frac{1}{25}x+\frac{3}{80}\left(x+5\right)=\frac{3}{4}$$

Use the distributive property to multiply \frac{3}{80} by x+5.

$$\frac{1}{25}x+\frac{3}{80}x+\frac{3}{80}\times 5=\frac{3}{4}$$

Express \frac{3}{80}\times 5 as a single fraction.

$$\frac{1}{25}x+\frac{3}{80}x+\frac{3\times 5}{80}=\frac{3}{4}$$

Multiply 3 and 5 to get 15.

$$\frac{1}{25}x+\frac{3}{80}x+\frac{15}{80}=\frac{3}{4}$$

Reduce the fraction \frac{15}{80} to lowest terms by extracting and canceling out 5.

$$\frac{1}{25}x+\frac{3}{80}x+\frac{3}{16}=\frac{3}{4}$$

Combine \frac{1}{25}x and \frac{3}{80}x to get \frac{31}{400}x.

$$\frac{31}{400}x+\frac{3}{16}=\frac{3}{4}$$

Subtract \frac{3}{16} from both sides.

$$\frac{31}{400}x=\frac{3}{4}-\frac{3}{16}$$

Least common multiple of 4 and 16 is 16. Convert \frac{3}{4} and \frac{3}{16} to fractions with denominator 16.

$$\frac{31}{400}x=\frac{12}{16}-\frac{3}{16}$$

Since \frac{12}{16} and \frac{3}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{31}{400}x=\frac{12-3}{16}$$

Subtract 3 from 12 to get 9.

$$\frac{31}{400}x=\frac{9}{16}$$

Multiply both sides by \frac{400}{31}, the reciprocal of \frac{31}{400}.

$$x=\frac{9}{16}\times \frac{400}{31}$$

Multiply \frac{9}{16} times \frac{400}{31} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{9\times 400}{16\times 31}$$

Do the multiplications in the fraction \frac{9\times 400}{16\times 31}.

$$x=\frac{3600}{496}$$

Reduce the fraction \frac{3600}{496} to lowest terms by extracting and canceling out 16.

$$x=\frac{225}{31}$$