Question

- 1/2 * y + 6 <= 2 what’s the answer

Answer 1

`y\ge 8`

Explanation:

We can solve for y in the inequality:

`-\frac12 \,y+ 6 \le 2`

with the following steps:

1. subtracting 6 from both sides

`-\frac12 \,y \le 2 - 6`

`-\frac12 \,y \le -4`

2. dividing both sides by -1/2 (and flipping the sign)

`y \ge -4/ \left(-\frac12\right)`

`y \ge -4 \cdot (-2)`

`\boxed{y\ge 8}`

Further Note

We flip the sign when dividing or multiplying by a negative because we are effectively swapping the sides. We could instead add
`y` and subtract
`-8` from both sides after dividing by the absolute value of
`y`'s coefficient:

`-y \le -4/ \frac12`

`-y \le -4 \cdot 2`

`-y \le -8 \\ \underline{+y} \ \ \ \ \underline{+y}`

`0 \le y-8`

`8 \le y`

`\implies y \ge 8`