-3(1-4x)+4(1-2x)=4x+1 — step-by-step solution

Let's solve in

ℝ

- 3 \cdot (1 - 4 x) + 4 \cdot (1 - 2 x) = 4 x + 1

- 3 \cdot (1 - 4 x)

+ 4 \cdot (1 - 2 x)

- 4 x

- 1 = 0

ⓘ Expand by multiplying each term inside the parentheses:

- 3 \cdot (1 - 4 x)

- (3 - 12 x)

4 \cdot (1 - 2 x)

4 - 8 x

- (3 - 12 x)

+ 4

- 8 x

- 4 x

- 1 = 0

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

- (3 - 12 x)

- 3 + 12 x

■Start from

4

and move back

1

on the number line:

4 - 1

3

■Like terms are grouped by adding their coefficients:

- 8 x - 4 x

-12 x

- 3

+ 12 x

+ 3

- 12 x = 0

ⓘ Start from

-3

and move forward

3

on the number line, up to zero:

- 3 + 3

0

■Like terms are grouped by adding their coefficients:

12 x - 12 x

0

0 + 0 = 0

ⓘ Adding 0 changes nothing:

0 + 0

0

0 = 0

▶Solution found:

x \in ℝ