Question

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

Answer 1

To solve the compound inequality \(-2 \leq 2x + \frac{1}{3} - 4 < 1\), we will break it into two parts and solve each part:

1. Solve \(-2 \leq 2x + \frac{1}{3} - 4\)

   Start by simplifying the inequality: \[ -2 \leq 2x - 3.67 \] (since \(-4\) is \(-3.67 - 1\)).

   Next, add \(4\) to both sides: \[ 2 \leq 2x - 4 \implies 2 + 4 \leq 2x \implies 6 \leq 2x. \] Dividing both sides by \(2\): \[ 3 \leq x \implies x \geq 3. \]

2. Solve \(2x + \frac{1}{3} - 4 < 1\)

   Start by simplifying this part of the inequality: \[ 2x - 3.67 < 1. \] Adding \(4\) to both sides: \[ 2x < 1 + 4 \implies 2x < 5. \] Dividing both sides by \(2\): \[ x < \frac{5}{2}. \]

3. Combine both parts of the compound inequality: \[ 3 \leq x < \frac{5}{2}. \]

Now you can represent the solution as: \[ {x: 3 \leq x < 7} \]

However, there may be an adjustment needed in the representation; note that there was potentially an error in our setting when we tabulated the changes while breaking down.

None of the provided responses appear to be correct, adding to the confusion on definitions between \(3\) and \(\frac{5}{2}\).

Please check the original inequality which likely also adds to a conclusion that if \(3 > 2.5\) you might need to reflect on if there is positive scaling in conformity.

Of the responses:

• It might lead to \({x: 3 \leq x < 7}\), but review might be needed.