Solve 0.4*(12.5+1/2x)=0.3(12.5+x)

$$0.4 \times ( 12.5 + \frac { 1 } { 2 } x ) = 0.3 ( 12.5 + x )$$

Solve for x

$$x=12.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply 0.4 by 12.5+\frac{1}{2}x.

$$5+0.4\times \frac{1}{2}x=0.3\left(12.5+x\right)$$

Convert decimal number 0.4 to fraction \frac{4}{10}. Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$5+\frac{2}{5}\times \frac{1}{2}x=0.3\left(12.5+x\right)$$

Multiply \frac{2}{5} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$5+\frac{2\times 1}{5\times 2}x=0.3\left(12.5+x\right)$$

Cancel out 2 in both numerator and denominator.

$$5+\frac{1}{5}x=0.3\left(12.5+x\right)$$

Use the distributive property to multiply 0.3 by 12.5+x.

$$5+\frac{1}{5}x=3.75+0.3x$$

Subtract 0.3x from both sides.

$$5+\frac{1}{5}x-0.3x=3.75$$

Combine \frac{1}{5}x and -0.3x to get -\frac{1}{10}x.

$$5-\frac{1}{10}x=3.75$$

Subtract 5 from both sides.

$$-\frac{1}{10}x=3.75-5$$

Subtract 5 from 3.75 to get -1.25.

$$-\frac{1}{10}x=-1.25$$

Multiply both sides by -10, the reciprocal of -\frac{1}{10}.

$$x=-1.25\left(-10\right)$$

Multiply -1.25 and -10 to get 12.5.

$$x=12.5$$