Solve 130*5%+x*9%/130+x=6.4/100

$$\frac { 130 \times 5 \% + x \times 9 \% } { 130 + x } = \frac { 6.4 } { 100 }$$

Solve for x

$$x=70$$

Steps for Solving Linear Equation

Variable x cannot be equal to -130 since division by zero is not defined. Multiply both sides of the equation by 100\left(x+130\right), the least common multiple of 130+x,100.

$$100\left(130\times \frac{5}{100}+x\times \frac{9}{100}\right)=\left(x+130\right)\times 6.4$$

Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$100\left(130\times \frac{1}{20}+x\times \frac{9}{100}\right)=\left(x+130\right)\times 6.4$$

Multiply 130 and \frac{1}{20} to get \frac{13}{2}.

$$100\left(\frac{13}{2}+x\times \frac{9}{100}\right)=\left(x+130\right)\times 6.4$$

Use the distributive property to multiply 100 by \frac{13}{2}+x\times \frac{9}{100}.

$$650+100x\times \frac{9}{100}=\left(x+130\right)\times 6.4$$

Multiply 100 and \frac{9}{100} to get 9.

$$650+9x=\left(x+130\right)\times 6.4$$

Use the distributive property to multiply x+130 by 6.4.

$$650+9x=6.4x+832$$

Subtract 6.4x from both sides.

$$650+9x-6.4x=832$$

Combine 9x and -6.4x to get 2.6x.

$$650+2.6x=832$$

Subtract 650 from both sides.

$$2.6x=832-650$$

Subtract 650 from 832 to get 182.

$$2.6x=182$$

Divide both sides by 2.6.

$$x=\frac{182}{2.6}$$

Expand \frac{182}{2.6} by multiplying both numerator and the denominator by 10.

$$x=\frac{1820}{26}$$

Divide 1820 by 26 to get 70.

$$x=70$$