Question

Determine whether each number is a solution of the inequality below.
4 x plus 3less than or equalsnegative 4
a. 1
b. 2
c. 3
Question content area bottom
Part 1
a. Is 1 a​ solution?
No
Yes

Answer 1

To determine whether each number is a solution of the inequality \( 4x + 3 \leq -4 \), we will substitute each value into the inequality and check if it holds true.

**Step 1: Solve the inequality**
We will first isolate \( x \) in the inequality:

1. Subtract 3 from both sides:
\[
4x + 3 - 3 \leq -4 - 3
\]
which simplifies to:
\[
4x \leq -7
\]

2. Divide both sides by 4:
\[
x \leq -\frac{7}{4}
\]

**Step 2: Check each value**

a. Checking if \( 1 \) is a solution:
\[
4(1) + 3 = 4 + 3 = 7
\]
Now check if \( 7 \leq -4 \):
- This is **false**.

b. Checking if \( 2 \) is a solution:
\[
4(2) + 3 = 8 + 3 = 11
\]
Now check if \( 11 \leq -4 \):
- This is **false**.

c. Checking if \( 3 \) is a solution:
\[
4(3) + 3 = 12 + 3 = 15
\]
Now check if \( 15 \leq -4 \):
- This is **false**.

**Conclusion:**
- a. **No**, \( 1 \) is not a solution.
- b. **No**, \( 2 \) is not a solution.
- c. **No**, \( 3 \) is not a solution.

In summary:
- a. Is 1 a solution? **No**
- b. Is 2 a solution? **No**
- c. Is 3 a solution? **No**