Solve 45/6+(2,75-(6,5x+7,5))-6,4x

$$4 \frac { 5 } { 6 } + ( 2,75 - ( 6,5 x + 7,5 ) ) - 6,4 x$$

Evaluate

$$-\frac{129x}{10}+\frac{1}{12}$$

Solution Steps

Multiply 4 and 6 to get 24.

$$\frac{24+5}{6}+2,75-\left(6,5x+7,5\right)-6,4x$$

Add 24 and 5 to get 29.

$$\frac{29}{6}+2,75-\left(6,5x+7,5\right)-6,4x$$

Convert decimal number 2,75 to fraction \frac{275}{100}. Reduce the fraction \frac{275}{100} to lowest terms by extracting and canceling out 25.

$$\frac{29}{6}+\frac{11}{4}-\left(6,5x+7,5\right)-6,4x$$

Least common multiple of 6 and 4 is 12. Convert \frac{29}{6} and \frac{11}{4} to fractions with denominator 12.

$$\frac{58}{12}+\frac{33}{12}-\left(6,5x+7,5\right)-6,4x$$

Since \frac{58}{12} and \frac{33}{12} have the same denominator, add them by adding their numerators.

$$\frac{58+33}{12}-\left(6,5x+7,5\right)-6,4x$$

Add 58 and 33 to get 91.

$$\frac{91}{12}-\left(6,5x+7,5\right)-6,4x$$

To find the opposite of 6,5x+7,5, find the opposite of each term.

$$\frac{91}{12}-6,5x-7,5-6,4x$$

Convert decimal number 7,5 to fraction \frac{75}{10}. Reduce the fraction \frac{75}{10} to lowest terms by extracting and canceling out 5.

$$\frac{91}{12}-6,5x-\frac{15}{2}-6,4x$$

Least common multiple of 12 and 2 is 12. Convert \frac{91}{12} and \frac{15}{2} to fractions with denominator 12.

$$\frac{91}{12}-6,5x-\frac{90}{12}-6,4x$$

Since \frac{91}{12} and \frac{90}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{91-90}{12}-6,5x-6,4x$$

Subtract 90 from 91 to get 1.

$$\frac{1}{12}-6,5x-6,4x$$

Combine -6,5x and -6,4x to get -12,9x.

$$\frac{1}{12}-12,9x$$

Expand

$$-\frac{129x}{10}+\frac{1}{12}$$

Solution Steps

Multiply 4 and 6 to get 24.

$$\frac{24+5}{6}+2,75-\left(6,5x+7,5\right)-6,4x$$

Add 24 and 5 to get 29.

$$\frac{29}{6}+2,75-\left(6,5x+7,5\right)-6,4x$$

Convert decimal number 2,75 to fraction \frac{275}{100}. Reduce the fraction \frac{275}{100} to lowest terms by extracting and canceling out 25.

$$\frac{29}{6}+\frac{11}{4}-\left(6,5x+7,5\right)-6,4x$$

Least common multiple of 6 and 4 is 12. Convert \frac{29}{6} and \frac{11}{4} to fractions with denominator 12.

$$\frac{58}{12}+\frac{33}{12}-\left(6,5x+7,5\right)-6,4x$$

Since \frac{58}{12} and \frac{33}{12} have the same denominator, add them by adding their numerators.

$$\frac{58+33}{12}-\left(6,5x+7,5\right)-6,4x$$

Add 58 and 33 to get 91.

$$\frac{91}{12}-\left(6,5x+7,5\right)-6,4x$$

To find the opposite of 6,5x+7,5, find the opposite of each term.

$$\frac{91}{12}-6,5x-7,5-6,4x$$

Convert decimal number 7,5 to fraction \frac{75}{10}. Reduce the fraction \frac{75}{10} to lowest terms by extracting and canceling out 5.

$$\frac{91}{12}-6,5x-\frac{15}{2}-6,4x$$

Least common multiple of 12 and 2 is 12. Convert \frac{91}{12} and \frac{15}{2} to fractions with denominator 12.

$$\frac{91}{12}-6,5x-\frac{90}{12}-6,4x$$

Since \frac{91}{12} and \frac{90}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{91-90}{12}-6,5x-6,4x$$

Subtract 90 from 91 to get 1.

$$\frac{1}{12}-6,5x-6,4x$$

Combine -6,5x and -6,4x to get -12,9x.

$$\frac{1}{12}-12,9x$$