Question

Which answer gives all the values of x for which the inequality 3x + 2 ≥ 9 − 4x is true

A). x ≥ 1
B). x > 1
C). x = 1
D). x ≤ 1

Answer 1

Which of the following is the correct solution to the inequality Cx + 4 ≤ 18, where C is a number greater than 0?

A). x ≤ 14 over C

B). x ≤ 14

C). Cx ≤ 14

D). C ≤ 14x

Answer 2

1. Which equation has the same solution for x as this equation: x−12=40?

A). 12 − x = 40

B). x2 = 14

C). x4 = 13

D). x +12 = −40

Answer 3

To solve the inequality \( 3x + 2 \geq 9 - 4x \), we can start by isolating \( x \).

1. First, add \( 4x \) to both sides:
\[
3x + 4x + 2 \geq 9
\]
This simplifies to:
\[
7x + 2 \geq 9
\]

2. Next, subtract \( 2 \) from both sides:
\[
7x \geq 7
\]

3. Finally, divide both sides by \( 7 \):
\[
x \geq 1
\]

So the solution to the inequality is \( x \geq 1 \).

The correct answer is:
**A). x ≥ 1**

Answer 4

To solve the inequality \( Cx + 4 \leq 18 \), we can isolate \( x \). Here are the steps:

1. Subtract \( 4 \) from both sides:
\[
Cx \leq 18 - 4
\]
This simplifies to:
\[
Cx \leq 14
\]

2. Next, divide both sides by \( C \) (since \( C \) is a positive number, the direction of the inequality does not change):
\[
x \leq \frac{14}{C}
\]

Thus, the correct expression for the solution is \( x \leq \frac{14}{C} \).

Given the options, the correct answer is:

**A). x ≤ \(\frac{14}{C}\)**

Answer 5

To find an equation with the same solution for \( x \) as the equation \( x - 12 = 40 \), we first solve the given equation.

1. Start with the equation:
\[
x - 12 = 40
\]

2. Add \( 12 \) to both sides:
\[
x = 40 + 12
\]
\[
x = 52
\]

Now, we need to check each of the options to see which one has the solution \( x = 52 \).

**A)** \( 12 - x = 40 \)

Rearranging gives:
\[
-x = 40 - 12 \rightarrow -x = 28 \rightarrow x = -28
\]
(Not the same solution)

**B)** \( x^2 = 14 \)

To find \( x \):
\[
x = \sqrt{14} \text{ or } x = -\sqrt{14}
\]
(Not the same solution)

**C)** \( x^4 = 13 \)

To find \( x \):
\[
x = \sqrt[4]{13} \text{ or } x = -\sqrt[4]{13} \text{ or } x = \sqrt[4]{13} \text{ or } x = -\sqrt[4]{13}
\]
(Not the same solution)

**D)** \( x + 12 = -40 \)

Rearranging:
\[
x = -40 - 12 \rightarrow x = -52
\]
(Not the same solution)

None of these equations have \( x = 52 \) as a solution. Therefore, it's possible that there's a mistake in the original question or the provided options. None of the options match the correct solution of \( x = 52 \).