-2(4y-7)+y>= 2y-(-5+y) — step-by-step solution

Let's solve in

ℝ

- 2 \cdot (4 y - 7) + y \geq 2 y - (- 5 + y)

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

- (- 5 + y)

5 - y

- 2 \cdot (4 y - 7) + y \geq 2 y + 5 - y

ⓘ Like terms are grouped by adding their coefficients:

2 y - y

y

- 2 \cdot (4 y - 7) + y \geq y + 5

ⓘ Expand by multiplying each term inside the parentheses:

- 2 \cdot (4 y - 7)

- (8 y - 14)

- (8 y - 14) + y \geq y + 5

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

- (8 y - 14)

- 8 y + 14

- 8 y + 14 + y \geq y + 5

ⓘ Like terms are grouped by adding their coefficients:

- 8 y + y

-7 y

- 7 y + 14 \geq y + 5

ⓘ We gather the terms in

y

on the right and the other terms on the left

14 - 5 \geq y + 7 y

ⓘ Start from

14

and move back

5

on the number line:

14 - 5

9

■Like terms are grouped by adding their coefficients:

y + 7 y

8 y

9 \geq 8 y

ⓘ Both sides are divided by

8

▶Solution found:

y \leq \frac{9}{8}

The numeric value of:

y \leq \frac{9}{8}

is:

▷

y \leq 1.125