Solve 1/4*34+3/4*25+x26/4

$$\frac { 1 } { 4 } \times 34 + \frac { 3 } { 4 } \times 25 + x \frac { 26 } { 4 }$$

Evaluate

$$\frac{13x}{2}+\frac{109}{4}$$

Solution Steps

Multiply \frac{1}{4} and 34 to get \frac{34}{4}.

$$\frac{34}{4}+\frac{3}{4}\times 25+x\times \frac{26}{4}$$

Reduce the fraction \frac{34}{4} to lowest terms by extracting and canceling out 2.

$$\frac{17}{2}+\frac{3}{4}\times 25+x\times \frac{26}{4}$$

Express \frac{3}{4}\times 25 as a single fraction.

$$\frac{17}{2}+\frac{3\times 25}{4}+x\times \frac{26}{4}$$

Multiply 3 and 25 to get 75.

$$\frac{17}{2}+\frac{75}{4}+x\times \frac{26}{4}$$

Least common multiple of 2 and 4 is 4. Convert \frac{17}{2} and \frac{75}{4} to fractions with denominator 4.

$$\frac{34}{4}+\frac{75}{4}+x\times \frac{26}{4}$$

Since \frac{34}{4} and \frac{75}{4} have the same denominator, add them by adding their numerators.

$$\frac{34+75}{4}+x\times \frac{26}{4}$$

Add 34 and 75 to get 109.

$$\frac{109}{4}+x\times \frac{26}{4}$$

Reduce the fraction \frac{26}{4} to lowest terms by extracting and canceling out 2.

$$\frac{109}{4}+x\times \frac{13}{2}$$

Factor

$$\frac{26x+109}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{109+26x}{4}$$

Consider 34+75+26x. Multiply and combine like terms.

$$26x+109$$

Rewrite the complete factored expression.

$$\frac{26x+109}{4}$$