Question

Solve for the variable in each inequality.(2 points)
4+x<2.25⋅8

x_ _



10−3y≤2−y

y_ _

Answer 1

Let's solve each inequality step by step.

1. **Solve for \( x \) in the inequality:**
\[
4 + x < 2.25 \cdot 8
\]

First, calculate \( 2.25 \cdot 8 \):
\[
2.25 \cdot 8 = 18
\]

Now we have:
\[
4 + x < 18
\]

Next, subtract 4 from both sides:
\[
x < 18 - 4
\]
\[
x < 14
\]

Thus, the solution for \( x \) is:
\[
x < 14
\]


2. **Solve for \( y \) in the inequality:**
\[
10 - 3y \leq 2 - y
\]

First, let's add \( 3y \) to both sides:
\[
10 \leq 2 - y + 3y
\]
\[
10 \leq 2 + 2y
\]

Next, subtract 2 from both sides:
\[
10 - 2 \leq 2y
\]
\[
8 \leq 2y
\]

Now, divide both sides by 2:
\[
4 \leq y
\]

This can be rewritten as:
\[
y \geq 4
\]

Thus, the solution for \( y \) is:
\[
y \geq 4
\]


In summary:
- For \( x \): \( x < 14 \)
- For \( y \): \( y \geq 4 \)