Question

consider the inequality
y-14<-25
which step is needed to solve this inequality?
a. add 14 to both sides of the inequality
b. subtract 14 to both sides of the inequality
c. divide 14 from both sides of the inequality
d. multiply 14 from both sides of the inequality
determine the solution to the inequality
a. y < -11
b. y < -1.79
c. y < -350
d. y < -39
how should the solution of the inequality be graphed?
a. open circle, shade right
b. open circle, shade left
c. closed circle, shade right
d. closed circle, shade left

Answer 1

To solve the inequality \( y - 14 < -25 \), we need to isolate \( y \).

### Step to solve the inequality:
1. **Add 14 to both sides of the inequality** (Option a).

So, we perform the following calculation:
\[
y - 14 + 14 < -25 + 14
\]
\[
y < -11
\]

### Solution to the inequality:
The answer is: **a. \( y < -11 \)**.

### How should the solution of the inequality be graphed?
Since the inequality is \( y < -11 \), we represent this on a number line:
- We use an **open circle** at -11 because the inequality does not include -11 (the less than sign indicates that -11 is not part of the solution).
- We shade to the **left** of -11 since the solution includes all values less than -11.

So the correct option is: **b. open circle, shade left**.