2-5(x+5)=3(x-2)-1 — step-by-step solution

Let's solve in

ℝ

2 - 5 \cdot (x + 5) = 3 \cdot (x - 2) - 1

ⓘ Expand by multiplying each term inside the parentheses:

- 5 \cdot (x + 5)

- (5 x + 25)

3 \cdot (x - 2)

3 x - 6

2 - (5 x + 25) = 3 x - 6 - 1

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

- (5 x + 25)

- 5 x - 25

■Start from

-6

and move back

1

more on the number line, away from zero:

- 6 - 1

-7

2 - 5 x - 25 = 3 x - 7

ⓘ Start from

2

and move back

25

on the number line, going below zero:

2 - 25

-23

- 23 - 5 x = 3 x - 7

ⓘ We gather the terms in

x

on the right and the other terms on the left

- 23 + 7 = 3 x + 5 x

ⓘ Start from

-23

and move forward

7

on the number line, getting closer to zero:

- 23 + 7

-16

■Like terms are grouped by adding their coefficients:

3 x + 5 x

8 x

-16 = 8 x

ⓘ Both sides are divided by

8

x = - \frac{16}{8}

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

8

, their greatest common divisor:

- \frac{16}{8}

-2

▶Solution obtained:

x = -2