How do you solve and graph #-5 < 2x + 1 < 4#?

First,we take away 1 from both sides:

To solve and graph the inequality -5 < 2x + 1 < 4:

1. Subtract 1 from all parts: -5 - 1 < 2x + 1 - 1 < 4 - 1 -6 < 2x < 3

2. Divide everything by 2: -6/2 < 2x/2 < 3/2 -3 < x < 3/2

3. The solution is: -3 < x < 3/2

To graph this on a number line:

• Place an open circle at -3 (since x is not equal to -3).
• Place an open circle at 3/2 (since x is not equal to 3/2).
• Draw a line segment between these two points.
• Shade the line segment between -3 and 3/2 to indicate that x is within this range but not including the endpoints.
• This represents the graph of -3 < x < 3/2 on a number line.

To solve the compound inequality -5 < 2x + 1 < 4, we need to isolate the variable x.

First, subtract 1 from all parts of the inequality: -5 - 1 < 2x + 1 - 1 < 4 - 1 -6 < 2x < 3

Next, divide all parts by 2: -6/2 < 2x/2 < 3/2 -3 < x < 3/2

Now, graph the solution on the number line: -3 |---o-------------------------o---| 3/2 -3 x 3/2

The open circles indicate that -3 and 3/2 are not included in the solution set, as they don't satisfy the original inequality. The shaded region between -3 and 3/2 represents all values of x that satisfy the inequality.