Question

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: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:−32≤x<1}

Answer 1

To solve the compound inequality \(-2 \leq 2x + 13 - 4 < 1\), let's simplify and solve both parts of the inequality step by step.

1. Combine like terms: \[-2 \leq 2x + 9 < 1\]

2. Separate the compound inequality into two inequalities: \[-2 \leq 2x + 9\] \[2x + 9 < 1\]

Solving the first inequality:

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

Subtract 9 from both sides: \[-2 - 9 \leq 2x\] \[-11 \leq 2x\]

Now, divide by 2: \[-\frac{11}{2} \leq x\] or \[x \geq -\frac{11}{2}\]

Solving the second inequality:

\[2x + 9 < 1\]

Subtract 9 from both sides: \[2x < 1 - 9\] \[2x < -8\]

Now, divide by 2: \[x < -4\]

Combine the results:

We have two inequalities:

1. \(x \geq -\frac{11}{2}\)
2. \(x < -4\)

Now we rewrite \(-\frac{11}{2}\) to check its relationship with -4: \[-\frac{11}{2} = -5.5\]

Thus, we need to find the intersection of \(x \geq -\frac{11}{2}\) and \(x < -4\). The critical interval where these conditions overlap is: \[-\frac{11}{2} \leq x < -4\]

This can be expressed in interval notation as: \[-\frac{11}{2} \leq x < -4\]

Conclusion:

Now we check the provided options to see which one matches the bounds we found.

None of the options given seem to correspond to this interval explicitly. However, if we're looking in terms of the form \( {x: a ≤ x < b} \), it seems like it would be \[ {-\frac{11}{2} \leq x < -4} \] If this option is present.

It's necessary to ensure the provided options match what has been calculated:

• The given options show intervals that do not seem to directly reflect the inequalities derived from the compound statement.

However, if numerical values were in a manner to properly confirm the accurate representation, the closest resemblance might be observable from a refined formulation of options laid out earlier.

Could you check the options given again for any misalignment or numeric inaccuracies? Directly analyzing, I observe, none match the expected compound solution's derived bounds precisely.