5y-2(4-y)=27+1-2(2y-4)-1 — step-by-step solution

1) Let's solve in

ℝ

5 y - 2 \cdot (4 - y) = 27

+ 1

- 2 \cdot (2 y - 4)

- 1

ⓘ Start from

27

and move forward

1

on the number line:

27 + 1

28

5 y - 2 \cdot (4 - y) = 28 - 2 \cdot (2 y - 4) - 1

ⓘ Start from

28

and move back

1

on the number line:

28 - 1

27

5 y - 2 \cdot (4 - y) = 27 - 2 \cdot (2 y - 4)

ⓘ Expand by multiplying each term inside the parentheses:

- 2 \cdot (4 - y)

- (8 + 2 \cdot (- y))

- 2 \cdot (2 y - 4)

- (4 y - 8)

5 y - (8 + 2 \cdot (- y)) = 27 - (4 y - 8)

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

- (8 + 2 \cdot (- y))

- 8 - 2 \cdot (- y)

- (4 y - 8)

- 4 y + 8

5 y - 8 - 2 \cdot (- y) = 27 - 4 y + 8

ⓘ Two minus signs cancel out:

-2 \cdot (- y)

2 y

■Start from

27

and move forward

8

on the number line:

27 + 8

35

5 y - 8 + 2 y = 35 - 4 y

ⓘ Like terms are grouped by adding their coefficients:

5 y + 2 y

7 y

7 y - 8 = 35 - 4 y

ⓘ We add

8

to both sides■Start from

35

and move forward

8

on the number line:

35 + 8

43

7 y = 43 - 4 y

ⓘ We add

4 y

to both sides

7 y + 4 y = 43

ⓘ Like terms are grouped by adding their coefficients:

7 y + 4 y

11 y

11 y = 43

ⓘ Both sides are divided by

11

▶Solution found:

y = \frac{43}{11}

2) The numeric value of:

y = \frac{43}{11}

equals:

▷

y = \approx 3.9091