Question

Which set expresses the solution to the compound inequality −2≤2x+13−4<1?(1 point)Responses{x:5/2≤x<1}left brace x colon Start Fraction 5 over 2 End Fraction less-than-or-equal-to x less than 1 right brace{x:3≤x<7}left brace x colon 3 less-than-or-equal-to x less than 7 right brace{x:5/2≤x<7}left brace x colon Start Fraction 5 over 2 End Fraction less-than-or-equal-to x less than 7 right brace{x:−3/2≤x<1}

Answer 1

To solve the compound inequality \(-2 \leq 2x + 13 - 4 < 1\), we can break it down into two parts:

1. \(-2 \leq 2x + 13 - 4\)
2. \(2x + 13 - 4 < 1\)

First, simplify \(2x + 13 - 4\):

\[ 2x + 9 \]

Now rewrite the compound inequalities:

1. \(-2 \leq 2x + 9\)
2. \(2x + 9 < 1\)

Now, solve each inequality separately.

Inequality 1: \(-2 \leq 2x + 9\)

Subtract 9 from both sides:

\[ -2 - 9 \leq 2x \] \[ -11 \leq 2x \]

Divide both sides by 2:

\[ -\frac{11}{2} \leq x \quad \text{or} \quad x \geq -\frac{11}{2} \]

Inequality 2: \(2x + 9 < 1\)

Subtract 9 from both sides:

\[ 2x < 1 - 9 \] \[ 2x < -8 \]

Divide both sides by 2:

\[ x < -4 \]

Summary of the Inequalities:

Now combining the results, we have:

\[ -\frac{11}{2} \leq x < -4 \]

Since \(-\frac{11}{2} = -5.5\) and \(-4\) is simply \(-4\), the solution can be expressed as:

\[ -5.5 \leq x < -4 \]

Set Notation:

The correct expression in set notation is:

\[ { x : -\frac{11}{2} \leq x < -4 } \]

Since this option doesn't appear explicitly in your response options, it seems there may have been a misunderstanding in possible values provided.

However, you can choose the closest option from your list, which should represent the range of x values suitable according to the inequalities you've provided, but it looks like none correspond to our solution properly.

If the solution choices are indeed those given, none of them fits the correct answer:

• The correct answer is {x : -\frac{11}{2} \leq x < -4}, which doesn't appear in your selections.