3(x-3)+1=5x-4+3(7-x) — step-by-step solution

Let's solve in

ℝ

3 \cdot (x - 3) + 1 = 5 x - 4 + 3 \cdot (7 - x)

ⓘ Expand by multiplying each term inside the parentheses:

3 \cdot (x - 3)

3 x - 9

3 \cdot (7 - x)

21 + 3 \cdot (- x)

3 x - 9 + 1 = 5 x

- 4

+ 21

+ 3 \cdot (- x)

ⓘ Start from

-9

and move forward

1

on the number line, getting closer to zero:

- 9 + 1

-8

■Start from

-4

and move forward

21

on the number line, going past zero:

- 4 + 21

17

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

3 \cdot (- x)

- 3 x

3 x - 8 = 5 x + 17 - 3 x

ⓘ Like terms are grouped by adding their coefficients:

5 x - 3 x

2 x

3 x - 8 = 2 x + 17

ⓘ We add

8

to both sides■Start from

17

and move forward

8

on the number line:

17 + 8

25

3 x = 2 x + 25

ⓘ We subtract

2 x

from both sides

3 x - 2 x = 25

ⓘ Like terms are grouped by adding their coefficients:

3 x - 2 x

x

▶Solution obtained:

x = 25