Which of the following equations has the solution set {−3}

Question

{
−
3
}
?(1 point)
Responses

4x−8=4
4
𝑥
−
8
=
4
4 x minus 8 equals 4

4x−8=−4
4
𝑥
−
8
=
−
4
4 x minus 8 equals negative 4

4x+8=−4
4
𝑥
+
8
=
−
4
4 x plus 8 equals negative 4

4x+8=4
4
𝑥
+
8
=
4
4 x plus 8 equals 4

Answer 1

To find which equation has the solution set \({-3}\), we will solve each equation for \(x\) and see which gives \(x = -3\).

1. Equation: \(4x - 8 = 4\)

   \[ 4x = 4 + 8 \ 4x = 12 \ x = \frac{12}{4} \ x = 3 \] (Not \(-3\))

2. Equation: \(4x - 8 = -4\)

   \[ 4x = -4 + 8 \ 4x = 4 \ x = \frac{4}{4} \ x = 1 \] (Not \(-3\))

3. Equation: \(4x + 8 = -4\)

   \[ 4x = -4 - 8 \ 4x = -12 \ x = \frac{-12}{4} \ x = -3 \] (This is \(-3\))

4. Equation: \(4x + 8 = 4\)

   \[ 4x = 4 - 8 \ 4x = -4 \ x = \frac{-4}{4} \ x = -1 \] (Not \(-3\))

The only equation that has the solution set \({-3}\) is:

\(4x + 8 = -4\).

Answer 2

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

{x:52≤x<1}
{
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:3≤x<7}
{
𝑥
:
3
≤
𝑥
<
7
}
left brace x colon 3 less-than-or-equal-to x less than 7 right brace

{x:52≤x<7}
{
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:−32≤x<1}
{
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

Answer 3

To solve the compound inequality \(-2 \leq 2x + 13 - 4 < 1\), we will simplify the middle expression and then break it into two separate inequalities to solve.

First, simplify the middle expression:

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

Now, we will split this into two inequalities:

1. Inequality 1: \(-2 \leq 2x + 9\)

   \[ -2 - 9 \leq 2x \ -11 \leq 2x \ -\frac{11}{2} \leq x \quad \text{or} \quad x \geq -\frac{11}{2} \]

2. Inequality 2: \(2x + 9 < 1\)

   \[ 2x < 1 - 9 \ 2x < -8 \ x < -4 \]

From these inequalities, we have:

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

This interval can be rewritten as:

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

Now we need to choose which option matches this solution set. Let's analyze the provided options:

1. \({x: \frac{5}{2} \leq x < 1}\) - This is not our solution.
2. \({x: 3 \leq x < 7}\) - This is not our solution.
3. \({x: \frac{5}{2} \leq x < 7}\) - This is not our solution.
4. \({x: -\frac{3}{2} \leq x < 1}\) - This is not our solution either.

None of the options seem to match the derived inequality \(-\frac{11}{2} \leq x < -4\). However, I made an error in transcribing the inequalities to the greatest extent.

The solution in fraction form was meant to conclude as set \(x : -\frac{11}{2} \leq x < -4\), which should mathematically match with either close comparisons or general understanding of options.

Given the correct form, please verify the denominations again or provide missing sets as there seems to be a disparity or format in thresholds requiring either additional verification or correction.