Solve 0.456=1/2*3.53+3.53x*0.5

$$0.456 = \frac{ 1 }{ 2 \cdot 3.53 } +3.53x \times 0.5$$

Solve for x

$$x=\frac{110968}{623045}\approx 0.178105915$$

Steps for Solving Linear Equation

Multiply 2 and 3.53 to get 7.06.

$$0.456=\frac{1}{7.06}+3.53x\times 0.5$$

Expand \frac{1}{7.06} by multiplying both numerator and the denominator by 100.

$$0.456=\frac{100}{706}+3.53x\times 0.5$$

Reduce the fraction \frac{100}{706} to lowest terms by extracting and canceling out 2.

$$0.456=\frac{50}{353}+3.53x\times 0.5$$

Multiply 3.53 and 0.5 to get 1.765.

$$0.456=\frac{50}{353}+1.765x$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{50}{353}+1.765x=0.456$$

Subtract \frac{50}{353} from both sides.

$$1.765x=0.456-\frac{50}{353}$$

Convert decimal number 0.456 to fraction \frac{456}{1000}. Reduce the fraction \frac{456}{1000} to lowest terms by extracting and canceling out 8.

$$1.765x=\frac{57}{125}-\frac{50}{353}$$

Least common multiple of 125 and 353 is 44125. Convert \frac{57}{125} and \frac{50}{353} to fractions with denominator 44125.

$$1.765x=\frac{20121}{44125}-\frac{6250}{44125}$$

Since \frac{20121}{44125} and \frac{6250}{44125} have the same denominator, subtract them by subtracting their numerators.

$$1.765x=\frac{20121-6250}{44125}$$

Subtract 6250 from 20121 to get 13871.

$$1.765x=\frac{13871}{44125}$$

Divide both sides by 1.765.

$$x=\frac{\frac{13871}{44125}}{1.765}$$

Express \frac{\frac{13871}{44125}}{1.765} as a single fraction.

$$x=\frac{13871}{44125\times 1.765}$$

Multiply 44125 and 1.765 to get 77880.625.

$$x=\frac{13871}{77880.625}$$

Expand \frac{13871}{77880.625} by multiplying both numerator and the denominator by 1000.

$$x=\frac{13871000}{77880625}$$

Reduce the fraction \frac{13871000}{77880625} to lowest terms by extracting and canceling out 125.

$$x=\frac{110968}{623045}$$