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Which set expresses the solution to the compound inequality −2≤2x+13−4<1?(1 point)

Responses

{x:52≤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:−32≤x<1}
left brace x colon Start Fraction negative 3 over 2 End Fraction less-than-or-equal-to x less than 1 right brace

{x:52≤x<7}

3 answers

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

  1. Start with the left part of the inequality: \[ -2 \leq 2x + 13 - 4 \] Simplifying gives: \[ -2 \leq 2x + 9 \] Subtracting 9 from both sides: \[ -11 \leq 2x \] Dividing by 2: \[ -\frac{11}{2} \leq x \quad \text{or} \quad x \geq -\frac{11}{2} \]

  2. Now, solve the right part of the inequality: \[ 2x + 13 - 4 < 1 \] Simplifying gives: \[ 2x + 9 < 1 \] Subtracting 9 from both sides: \[ 2x < -8 \] Dividing by 2: \[ x < -4 \]

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

Since \(-\frac{11}{2} = -5.5\), we can express the solution as: \[ -\frac{11}{2} \leq x < -4 \]

Now let's find the corresponding option in the responses:

  • \( { x : -\frac{3}{2} \leq x < 1 } \) is not correct.
  • \( { x : 3 \leq x < 7 } \) is not correct.
  • \( { x : -\frac{11}{2} \leq x < -4 } \) is correct but given incorrectly in the response form.
  • \( { x : -\frac{5}{2} \leq x < 7 } \) does not match.

In conclusion, none of the provided options seem to express the correct solution. The correct answer, based on the solved inequalities, is: \[ { x : -\frac{11}{2} \leq x < -4 } \]

Since it's not one of the answers, please double-check the options you provided.

Pick the answer that is most right

Given the solutions derived from the compound inequality \(-2 \leq 2x + 13 - 4 < 1\), we found:

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

However, none of the provided responses exactly match this solution. The closest option that can be considered is:

\({ x : -\frac{3}{2} \leq x < 1 }\)

Although it's not the correct range, it is the only one listed that is formatted correctly as a set notation, while others are completely incorrect.

If the goal is to choose the best available option despite it not being fully accurate, select:

\({ x : -\frac{3}{2} \leq x < 1 }\)

Please note that while this is the most correctly formatted response, it does not reflect the correct solution to the inequality.