(x-1)/4-(12-2x)/5 =(x-2)/5 — step-by-step solution

1) Let's solve in

ℝ

\frac{x - 1}{4} - \frac{12 - 2 x}{5} = \frac{x - 2}{5}

ⓘ The minus sign of the fraction goes into the numerator or the denominator, changing the sign of each of its terms:

- \frac{12 - 2 x}{5}

\frac{- 12 + 2 x}{5}

\frac{x - 1}{4} + \frac{- 12 + 2 x}{5} = \frac{x - 2}{5}

2) Let's sum the fractions:

\frac{x - 1}{4} + \frac{- 12 + 2 x}{5} - \frac{x - 2}{5} = 0

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

\frac{x - 1}{4} + \frac{- 12 + 2 x}{5}

\frac{(x - 1) \cdot 5 + (- 12 + 2 x) \cdot 4}{4 \cdot 5}

■The minus sign of the fraction goes into the numerator or the denominator, changing the sign of each of its terms:

- \frac{x - 2}{5}

\frac{- x + 2}{5}

\frac{(x - 1) \cdot 5 + (- 12 + 2 x) \cdot 4}{4 \cdot 5} + \frac{- x + 2}{5} = 0

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

\frac{(x - 1) \cdot 5 + (- 12 + 2 x) \cdot 4}{20} + \frac{- x + 2}{5}

\frac{((x - 1) \cdot 5 + (- 12 + 2 x) \cdot 4) + (- x + 2) \cdot 4}{20}

ⅰ

4 \cdot 5

20

\frac{((x - 1) \cdot 5 + (- 12 + 2 x) \cdot 4) + (- x + 2) \cdot 4}{20} = 0

\frac{(x - 1) \cdot 5 + (- 12 + 2 x) \cdot 4 + (- x + 2) \cdot 4}{20} = 0

Let's solve in

ℝ

(x - 1) \cdot 5 + (- 12 + 2 x) \cdot 4 + (- x + 2) \cdot 4 = 0

ⓘ Expand by multiplying each term inside the parentheses:

(x - 1) \cdot 5

x \cdot 5 - 5

(- 12 + 2 x) \cdot 4

- 48 + 8 x

(- x + 2) \cdot 4

- x \cdot 4 + 8

x \cdot 5

- 5

- 48

+ 8 x

- x \cdot 4

+ 8 = 0

ⓘ Start from

-5

and move back

48

more on the number line, away from zero:

- 5 - 48

-53

■Like terms are grouped by adding their coefficients:

x \cdot 5 + 8 x - x \cdot 4

9 x

9 x - 53 + 8 = 0

ⓘ Start from

-53

and move forward

8

on the number line, getting closer to zero:

- 53 + 8

-45

9 x - 45 = 0

ⓘ We add

45

to both sides

9 x = 45

ⓘ Both sides are divided by

9

x = \frac{45}{9}

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

9

, their greatest common divisor:

\frac{45}{9}

5

▶Solution obtained:

x = 5