5(2+x)-x=10+4(x+1) — step-by-step solution

Let's solve in

ℝ

5 \cdot (2 + x) - x = 10 + 4 \cdot (x + 1)

5 \cdot (2 + x)

- x

- 10

- 4 \cdot (x + 1) = 0

ⓘ Expand by multiplying each term inside the parentheses:

5 \cdot (2 + x)

10 + 5 x

- 4 \cdot (x + 1)

- (4 x + 4)

10

+ 5 x

- x

- 10

- (4 x + 4) = 0

ⓘ Start from

10

and move back

10

on the number line, down to zero:

10 - 10

0

■Like terms are grouped by adding their coefficients:

5 x - x

4 x

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

- (4 x + 4)

- 4 x - 4

0

+ 4 x

- 4 x

- 4 = 0

ⓘ Adding 0 changes nothing:

0 + 4 x

4 x

■Like terms are grouped by adding their coefficients:

4 x - 4 x

0

0 - 4 = 0

ⓘ Adding 0 changes nothing:

0 - 4

-4

-4 = 0

The statement

-4 = 0

is false, whatever the value of

x

▶Solution:

x \in \emptyset