Question

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

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 side: \[ -2 \leq 2x + 13 - 4 \] This simplifies to: \[ -2 \leq 2x + 9 \] Then, we isolate \( x \): \[ -2 - 9 \leq 2x \] \[ -11 \leq 2x \] Dividing both sides by 2 gives: \[ -\frac{11}{2} \leq x \] or \[ x \geq -\frac{11}{2} \]

2. Solve the right side: \[ 2x + 13 - 4 < 1 \] This simplifies to: \[ 2x + 9 < 1 \] Isolate \( x \): \[ 2x < 1 - 9 \] \[ 2x < -8 \] Dividing both sides by 2 gives: \[ x < -4 \]

Now we can combine these two results:

The compound inequality is: \[ -\frac{11}{2} \leq x < -4 \]

In decimal form: \(-\frac{11}{2} = -5.5\).

This means we are looking for \( x \) values that satisfy: \[ -5.5 \leq x < -4 \]

Now let's match the resulting set to one of the provided options:

• {x: \(-\frac{3}{2} \leq x < 1\)} does not match our solution set.
• {x: \(3 \leq x < 7\)} does not match.
• {x: \(5/2 \leq x < 7\)} does not match.
• {x: \(-32 \leq x < 1\)} also does not match.

None of the given options correctly represent the solution \(-\frac{11}{2} \leq x < -4\). The correct representation isn't listed in the options provided.

Therefore, ensure to double check the inequality transformations and the final solutions before confirming the answer set against the provided options.