Solve (3+r)0.35=1.42-0.35/0.5

$$( 3 + r ) 0.35 = \frac { 1.42 - 0.35 } { 0.5 }$$

Solve for r

$$r = \frac{109}{35} = 3\frac{4}{35} \approx 3.114285714$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3+r by 0.35.

$$1.05+0.35r=\frac{1.42-0.35}{0.5}$$

Subtract 0.35 from 1.42 to get 1.07.

$$1.05+0.35r=\frac{1.07}{0.5}$$

Expand \frac{1.07}{0.5} by multiplying both numerator and the denominator by 100.

$$1.05+0.35r=\frac{107}{50}$$

Subtract 1.05 from both sides.

$$0.35r=\frac{107}{50}-1.05$$

Convert decimal number 1.05 to fraction \frac{105}{100}. Reduce the fraction \frac{105}{100} to lowest terms by extracting and canceling out 5.

$$0.35r=\frac{107}{50}-\frac{21}{20}$$

Least common multiple of 50 and 20 is 100. Convert \frac{107}{50} and \frac{21}{20} to fractions with denominator 100.

$$0.35r=\frac{214}{100}-\frac{105}{100}$$

Since \frac{214}{100} and \frac{105}{100} have the same denominator, subtract them by subtracting their numerators.

$$0.35r=\frac{214-105}{100}$$

Subtract 105 from 214 to get 109.

$$0.35r=\frac{109}{100}$$

Divide both sides by 0.35.

$$r=\frac{\frac{109}{100}}{0.35}$$

Express \frac{\frac{109}{100}}{0.35} as a single fraction.

$$r=\frac{109}{100\times 0.35}$$

Multiply 100 and 0.35 to get 35.

$$r=\frac{109}{35}$$