-31-4x=-5-5(1+5x) — step-by-step solution

Let's solve in

ℝ

- 31 - 4 x = - 5 - 5 \cdot (1 + 5 x)

ⓘ Expand by multiplying each term inside the parentheses:

- 5 \cdot (1 + 5 x)

- (5 + 25 x)

- 31 - 4 x = - 5 - (5 + 25 x)

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

- (5 + 25 x)

- 5 - 25 x

- 31 - 4 x = - 5 - 5 - 25 x

ⓘ Start from

-5

and move back

5

more on the number line, away from zero:

- 5 - 5

-10

- 31 - 4 x = - 10 - 25 x

ⓘ We add

31

to both sides■Start from

-10

and move forward

31

on the number line, going past zero:

- 10 + 31

21

- 4 x = 21 - 25 x

ⓘ We add

25 x

to both sides

- 4 x + 25 x = 21

ⓘ Like terms are grouped by adding their coefficients:

- 4 x + 25 x

21 x

21 x = 21

ⓘ Both sides are divided by

21

x = \frac{21}{21}

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

21

, their greatest common divisor:

\frac{21}{21}

1

▶Solution obtained:

x = 1