Question

Which set expresses the solution to the compound inequality −2≤2x+13−4<1?(1 point)Responses{x:−3/2≤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: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: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≤x<7}

Answer 1

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

1. Solve the left part: \(-2 \leq 2x + 13 - 4\)
2. Solve the right part: \(2x + 13 - 4 < 1\)

Starting with the left part:

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

\[ -2 - 9 \leq 2x \] \[ -11 \leq 2x \] Divide both sides by 2:

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

Now for the right part:

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

\[ 2x < 1 - 9 \] \[ 2x < -8 \] Divide both sides by 2:

\[ x < -4 \]

Now we combine the results from both parts:

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

To express this correctly in interval notation:

Since \(-\frac{11}{2} = -5.5\), the final solution is:

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

Now looking at the options you provided, none of them match this solution. If you meant the values were calculated or framed differently, please double-check calculations against choices provided or clarify any additional constraints. However, based on the calculation done, the correct solution set for the compound inequality is:

\({x: -\frac{11}{2} \leq x < -4}\).