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

?(2 points)
Responses

{x: 3≤x<7}
{x: 3≤x<7}

{x: 52≤x<7}
{x: 52≤x<7}

{x: −32≤x<1}
{x: −32≤x<1}

{x: 52≤x<1}

1 answer

To solve the compound inequality \(-2 \leq 2x + 13 - 4 < 1\), we first simplify the expression in the middle:

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

Now, we can break this into two separate inequalities to solve:

  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 both sides by 2:

\[ -\frac{11}{2} \leq x \quad \text{or} \quad x \geq -5.5 \]

Solving the second inequality:

\(2x + 9 < 1\)

Subtract 9 from both sides:

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

Now, divide both sides by 2:

\[ x < -4 \]

Combining both solutions:

So, we have the two inequalities combined:

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

In decimal form, this is:

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

From the provided responses, none of them match this solution exactly. However, it appears that based on numerical ranges and choices given, it seems like there might be a misunderstanding in matching inequalities. Please double-check the values provided in your options against the computed ranges. If the provided responses remain as listed, they do not represent the solution to the compound inequality you provided.