Question

Solve the inequality for x and identify the graph of its solution.

3(x + 1) < 6
Choose the answer that gives both the correct solution and the correct graph.​

Answer 1

the answer is B

hope the answer may help you

Answer 2

To solve
`\(3|x + 1| < 6\)`, isolate the absolute value, create two cases, and combine solutions. The correct answer is
`\( -3 < x < 1\)`, and the appropriate choice is D.

Let's solve the inequality step by step:

`\[3|x + 1| < 6\]`

1. Isolate the Absolute Value:

`\[ |x + 1| < 2 \]`

2. Create Two Cases:

- Case one:
`\(x + 1 < 2\)`

`\[ x < 1 \]`

- Case two:
`\(x + 1 > -2\)`

`\[ x > -3 \]`

3. Combine the Solutions:

- Combine the solutions from both cases:

`\[ -3 < x < 1 \]`

Now, let's look at the choices:

A.
`\(x < -3\)` or
`\(x > 1\)` - Incorrect

B.
`\(x > -3\)` and
`\(x < 1\)` - Incorrect

C.
`\(x < -1\)` or
`\(x > 3\)` - Incorrect

D.
`\(x > -3\)` and
`\(x < 1\)` - Correct (it marks the interval from -
`3` to
`1`)

So, the correct solution is
`\( -3 < x < 1 \)`, and D marks the interval from -
`3` to
`1`, so D is the correct choice.