65/100*x+20/100*8= 85/100*8+x — step-by-step solution

1) Let's solve in

ℝ

\frac{65}{100} \cdot x + \frac{20}{100} \cdot 8 = \frac{85}{100} \cdot 8 + x

We simplify the fraction:

\frac{20}{100}

by the common factor:

20

to get the new quotient:

\frac{1}{5}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

5

, their greatest common divisor:

\frac{85}{100}

\frac{17 \cdot 5}{20 \cdot 5}

\frac{17}{20}

\frac{13}{20} \cdot x + \frac{1}{5} \cdot 8 = \frac{17}{20} \cdot 8 + x

ⓘ Multiplying a fraction by a term multiplies its numerator:

\frac{13}{20} \cdot x

\frac{13 x}{20}

■Multiplying a fraction by a number multiplies its numerator:

\frac{1}{5} \cdot 8

\frac{1 \cdot 8}{5}

\frac{8}{5}

\frac{17}{20} \cdot 8

\frac{17 \cdot 8}{20}

\frac{136}{20}

■To add fractions, put them over the same denominator, then add the numerators:

\frac{13 x}{20} + \frac{8}{5}

\frac{13 x + 4 \cdot 8}{20}

\frac{13 x + 4 \cdot 8}{20} = \frac{136}{20} + x

ⓘ Multiplications are done before additions and subtractions:

4 \cdot 8

32

■We simplify the fraction by dividing the numerator and the denominator by

4

, their greatest common divisor:

\frac{136}{20}

\frac{34 \cdot 4}{5 \cdot 4}

\frac{34}{5}

\frac{13 x + 32}{20} = \frac{34}{5} + x

2) Let's sum the fractions:

\frac{13 x + 32}{20} - \frac{34}{5} - x = 0

ⅰ

\frac{13 x + 32}{20} - x

\frac{(13 x + 32) + 20 \cdot (- x)}{20}

\frac{(13 x + 32) + 20 \cdot (- x)}{20} - \frac{34}{5} = 0

ⓘ The minus sign is placed in front of the product:

20 \cdot (- x)

- 20 x

■To add fractions, put them over the same denominator, then add the numerators:

\frac{13 x + 32 - 20 x}{20} - \frac{34}{5}

\frac{(13 x + 32 - 20 x) - 34 \cdot 4}{20}

\frac{(13 x + 32 - 20 x) - 34 \cdot 4}{20} = 0

ⓘ Like terms are grouped by adding their coefficients:

13 x - 20 x

-7 x

■Multiplications are done before additions and subtractions:

34 \cdot 4

(30 + 4) \cdot 4

30 \cdot 4 + 4 \cdot 4

120 + 16

136

\frac{- 7 x + 32 - 136}{20} = 0

ⓘ The numerator and the denominator are computed before the division:

32 - 136

-104

\frac{- 7 x - 104}{20} = 0

ⓘ The minus sign is factored out, changing the sign of each term:

- 7 x - 104

- (7 x + 104)

- \frac{7 x + 104}{20} = 0

Let's solve in

ℝ

- (7 x + 104) = 0

ⓘ A minus sign before a parenthesis changes the sign of each of its terms:

- (7 x + 104)

- 7 x - 104

- 7 x - 104

- 7 x = 104

ⓘ Both sides are divided by

-7

x = \frac{104}{-7}

ⓘ The sign of a fraction goes in front of the bar, whether it comes from the numerator or the denominator:

\frac{104}{-7}

- \frac{104}{7}

▶Solution found:

x = - \frac{104}{7}

3) The numeric value of:

x = - \frac{104}{7}

equals:

▷

x = \approx -14.8571