Question

Question content area top
Part 1
Determine whether each number is a solution of the inequality below.
5 x plus 4less thannegative 1
a. 1
b. negative 2
c. 2
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 \(5x + 4 < -1\), we will substitute each number into the inequality and check if the inequality holds true.

First, let’s rewrite the inequality for clarity:

\[5x + 4 < -1\]

Now, we can solve this inequality for \(x\):

1. Subtract 4 from both sides:
\[5x < -1 - 4\]
\[5x < -5\]

2. Divide both sides by 5:
\[x < -1\]

Now, let's check each of the given numbers:

a. **1**:
\[5(1) + 4 < -1\]
\[5 + 4 < -1\]
\[9 < -1\] (This is **false**)

b. **-2**:
\[5(-2) + 4 < -1\]
\[-10 + 4 < -1\]
\[-6 < -1\] (This is **true**)

c. **2**:
\[5(2) + 4 < -1\]
\[10 + 4 < -1\]
\[14 < -1\] (This is **false**)

Now we summarize:

- a. Is **1** a solution? **No**
- b. Is **-2** a solution? **Yes**
- c. Is **2** a solution? **No**

If you have further questions or need more assistance, feel free to ask!