6(-y+4)-3(2y-3)=-y+5+5y — step-by-step solution

Let's solve in

ℝ

6 \cdot (- y + 4) - 3 \cdot (2 y - 3) = - y + 5 + 5 y

ⓘ Like terms are grouped by adding their coefficients:

- y + 5 y

4 y

6 \cdot (- y + 4) - 3 \cdot (2 y - 3) = 4 y + 5

ⓘ Expand by multiplying each term inside the parentheses:

6 \cdot (- y + 4)

6 \cdot (- y) + 24

- 3 \cdot (2 y - 3)

- (6 y - 9)

6 \cdot (- y) + 24 - (6 y - 9) = 4 y + 5

ⓘ The minus sign is placed in front of the product:

6 \cdot (- y)

- 6 y

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

- (6 y - 9)

- 6 y + 9

- 6 y

+ 24

- 6 y

+ 9 = 4 y + 5

ⓘ Start from

24

and move forward

9

on the number line:

24 + 9

33

■Like terms are grouped by adding their coefficients:

- 6 y - 6 y

-12 y

- 12 y + 33 = 4 y + 5

ⓘ We gather the terms in

y

on the right and the other terms on the left

33 - 5 = 4 y + 12 y

ⓘ Start from

33

and move back

5

on the number line:

33 - 5

28

■Like terms are grouped by adding their coefficients:

4 y + 12 y

16 y

28 = 16 y

ⓘ Both sides are divided by

16

y = \frac{28}{16}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

4

, their greatest common divisor:

\frac{28}{16}

\frac{7 \cdot 4}{4 \cdot 4}

\frac{7}{4}

▶Solution found:

y = \frac{7}{4}

The numeric value of:

y = \frac{7}{4}

is:

▷

y = 1.75