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

Let's solve in

ℝ

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

4 \cdot (x + 1)

- x

- 3 \cdot (x - 1)

- 3 = 0

ⓘ Expand by multiplying each term inside the parentheses:

4 \cdot (x + 1)

4 x + 4

- 3 \cdot (x - 1)

- (3 x - 3)

4 x

+ 4

- x

- (3 x - 3)

- 3 = 0

ⓘ Like terms are grouped by adding their coefficients:

4 x - x

3 x

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

- (3 x - 3)

- 3 x + 3

3 x

+ 4

- 3 x

+ 3

- 3 = 0

ⓘ Like terms are grouped by adding their coefficients:

3 x - 3 x

0

■Start from

3

and move back

3

on the number line, down to zero:

3 - 3

0

0 + 4 + 0 = 0

ⓘ Adding 0 changes nothing:

0 + 4 + 0

4

4 = 0

The statement

4 = 0

is false, whatever the value of

x

▶Solution:

x \in \emptyset