2(2-3x)-3(3-2x)=4(x+1)+3(4-5x)

Let's solve in

ℝ

2 \cdot (2 - 3 x) - 3 \cdot (3 - 2 x) = 4 \cdot (x + 1) + 3 \cdot (4 - 5 x)

ⓘ Expand by multiplying each term inside the parentheses:

2 \cdot (2 - 3 x)

4 - 6 x

- 3 \cdot (3 - 2 x)

- (9 - 6 x)

4 \cdot (x + 1)

4 x + 4

3 \cdot (4 - 5 x)

12 - 15 x

4 - 6 x - (9 - 6 x) = 4 x

+ 4

+ 12

- 15 x

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

- (9 - 6 x)

- 9 + 6 x

■Start from

4

and move forward

12

on the number line:

4 + 12

16

■Like terms are grouped by adding their coefficients:

4 x - 15 x

-11 x

4

- 6 x

- 9

+ 6 x = - 11 x + 16

ⓘ Start from

4

and move back

9

on the number line, going below zero:

4 - 9

-5

■Like terms are grouped by adding their coefficients:

- 6 x + 6 x

0

- 5 + 0 = - 11 x + 16

ⓘ Adding 0 changes nothing:

- 5 + 0

-5

-5 = - 11 x + 16

ⓘ We add

5

to both sides■Start from

16

and move forward

5

on the number line:

16 + 5

21

0 = - 11 x + 21

ⓘ We add

21

to both sides

11 x = 21

ⓘ Both sides are divided by

11

▶Solution found:

x = \frac{21}{11}

The numeric value of:

x = \frac{21}{11}

is:

▷

x = \approx 1.9091