Question

10. Solve -4 < x + 1 <3, and graph the answer on the number line.

Answer 1

The solution to the compound inequality -4 < x + 1 < 3 is -5 < x < 2, and it is represented on the number line as an open interval between -5 and 2, excluding the endpoints.

To solve the compound inequality -4 < x + 1 < 3, we'll break it down into two separate inequalities:

-4 < x + 1

x + 1 < 3

For the first inequality, subtract 1 from both sides:

-4 - 1 < x

-5 < x

For the second inequality, subtract 1 from both sides:

x + 1 - 1 < 3 - 1

x < 2

Combining the results, we get -5 < x < 2. This represents the solution to the original compound inequality.

Now, let's graph this solution on a number line. Marking -5 and 2 on the line, we indicate that x falls within the interval (-5, 2), excluding the endpoints. This is because the original inequality was strict (less than, not less than or equal to).

Answer 2

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given inequality

STEP 4: Solve the second part

`\begin{gathered} x+1\le \:3 \\ Subtract\text{ 1 from both sides} \\ x+1-1\leq3-1 \\ x\leq2 \end{gathered}`

STEP 5: Combine the intervals

[tex]\begin{gathered} Merge\text{ Overlapping intervals} \\ -5

Graph the answer: