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

Let's solve in

ℝ

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

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

- (x - 3)

- x + 3

4 \cdot (x - 5) - 5 \cdot (x - 4) = x

+ 4

- x

+ 3

ⓘ Start from

4

and move forward

3

on the number line:

4 + 3

7

■Like terms are grouped by adding their coefficients:

x - x

0

4 \cdot (x - 5) - 5 \cdot (x - 4) = 0 + 7

ⓘ Adding 0 changes nothing:

0 + 7

7

4 \cdot (x - 5) - 5 \cdot (x - 4) = 7

ⓘ Expand by multiplying each term inside the parentheses:

4 \cdot (x - 5)

4 x - 20

- 5 \cdot (x - 4)

- (5 x - 20)

4 x - 20 - (5 x - 20) = 7

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

- (5 x - 20)

- 5 x + 20

4 x

- 20

- 5 x

+ 20 = 7

ⓘ Start from

-20

and move forward

20

on the number line, up to zero:

- 20 + 20

0

■Like terms are grouped by adding their coefficients:

4 x - 5 x

- x

- x + 0 = 7

ⓘ Adding 0 changes nothing:

- x + 0

- x

- x = 7

ⓘ The sign of both sides is changed

▶Solution obtained:

x = -7