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

Question

?(1 point)
Responses

{x:52≤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≤x<7}
left brace x colon 3 less-than-or-equal-to x less than 7 right brace

{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:−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

Answer 1

To solve the compound inequality \(-2 \leq 2x + 13 - 4 < 1\), let's start by simplifying it.

First, simplify the middle expression:

\[ -2 \leq 2x + 9 < 1 \]

Now, we will split this into two separate inequalities:

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

Solving the first inequality:

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

Subtract 9 from both sides:

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

Now, divide by 2:

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

Solving the second inequality:

\[ 2x + 9 < 1 \]

Subtract 9 from both sides:

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

Now, divide by 2:

\[ x < -4 \]

Combining the results:

From the two inequalities we have:

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

To express \(-\frac{11}{2}\) as a decimal:

\(-\frac{11}{2} = -5.5\)

So we can rewrite the combined result as:

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

Interpreting the range:

Thus, the solution set represents all \(x\) values from \(-5.5\) to \(-4\), which does not correspond to any of the provided sets.

However, since \( -\frac{11}{2} \) (or \( 5/2 \) if transposed incorrectly) doesn't seem to appear in your provided solutions, it appears that the options available don't directly match.

Among your responses, none match the inequalities obtained from the problem. Please verify the inequalities or choices.