use inverse operations to solve for y: y+8>10

Question

y<2
y>18
y<18
y>2

Answer 1

Let's solve the inequality step by step using inverse operations.

Starting with the first inequality:

1. \( y + 8 > 10 \)

To isolate \( y \), subtract 8 from both sides:

\[ y + 8 - 8 > 10 - 8 \] \[ y > 2 \]

So the solution to the first inequality is:

\[ y > 2 \]

Now, let's examine the other inequalities listed:

2. \( y < 2 \): This means \( y \) is less than 2.
3. \( y > 18 \): This means \( y \) is greater than 18.
4. \( y < 18 \): This means \( y \) is less than 18.
5. \( y > 2 \): This matches our first inequality.

Now, let's summarize what we have:

• From the first inequality, \( y > 2 \).
• The second inequality \( y < 2 \) contradicts our first solution.
• The third inequality \( y > 18 \) does not contradict \( y > 2 \).
• The fourth inequality \( y < 18 \) still does not provide a complete range as it depends on other conditions.
• The last inequality \( y > 2 \) reaffirms our first solution.

Since we recognize that \( y < 2 \) contradicts \( y > 2 \), the solutions presented cannot all hold true simultaneously as they contradict one another.

The valid solution, based on the information given, is:

\[ y > 2 \quad \text{and} \quad y < 18 \quad \Rightarrow \quad 2 < y < 18 \]

So, if we were to combine the valid inequalities, the overall solution would be:

\[ 2 < y < 18 \quad \text{or} \quad y \in (2, 18) \]

Answer 2

which one

Answer 3

Apologies for the confusion. Let's clarify the inequalities:

1. \( y + 8 > 10 \) translates to \( y > 2 \).
2. \( y < 2 \) contradicts with \( y > 2 \).
3. \( y > 18 \) is a separate statement and does not interact with \( y < 2 \) or \( y > 2 \).
4. \( y < 18 \) does provide an upper limit to the values \( y \) can take.
5. \( y > 2 \) reaffirms the first inequality.

Given all these inequalities:

• \( y > 2 \) and \( y < 2 \) cannot be true simultaneously.
• Therefore, the system has no solution because the first two inequalities contradict each other.

So, no value of \( y \) satisfies all the given conditions.

If we only consider non-contradicting conditions, we can state:

• From \( y > 2 \) and \( y < 18 \), you can only conclude:

\[ 2 < y < 18 \]

However, since \( y < 2 \) and \( y > 18 \) cannot both coexist with \( y > 2 \) as true, the most straightforward conclusion is that there is no overall solution that can satisfy all inequalities together as given.

Thus, the answer is:

No solution.

Answer 4

pick one of the answers

Answer 5

Sure! Among the inequalities listed:

1. \( y + 8 > 10 \) leads to \( y > 2 \).
2. \( y < 2 \) contradicts the first.
3. \( y > 18 \) is independent and means \( y \) is greater than 18.
4. \( y < 18 \) means \( y \) is less than 18.
5. \( y > 2 \) reaffirms the first.

Since we need to pick one of the options provided, I will choose:

\( y > 2 \).

This inequality is derived from the first condition and does not contradict any other condition except for the second one. However, since it leads to a valid range when considered with the fourth inequality \( y < 18 \), it provides useful information.

So, the chosen answer is:

\( y > 2 \).

Answer 6

Solve x+14<25 . Make sure to write your inequality so that x comes first.

Answer 7

To solve the inequality \( x + 14 < 25 \) and rewrite it so that \( x \) comes first, follow these steps:

1. Subtract 14 from both sides of the inequality:

\[ x + 14 - 14 < 25 - 14 \]

2. Simplifying this gives:

\[ x < 11 \]

Now, to write the inequality so that \( x \) comes first, we can simply write:

\[ x < 11 \]

So, the final answer is:

\( x < 11 \).

Answer 8

Solve x−8≥5 . Make sure to write your inequality so that x comes first.

Answer 9

To solve the inequality \( x - 8 \geq 5 \) and write it so that \( x \) comes first, follow these steps:

1. Add 8 to both sides of the inequality:

\[ x - 8 + 8 \geq 5 + 8 \]

2. Simplifying this gives:

\[ x \geq 13 \]

Now, the inequality already has \( x \) first, so we can state it directly:

\( x \geq 13 \).

Answer 10

Solve x+10.5<20.2 . Make sure to write your inequality so that x comes first.

Answer 11

To solve the inequality \( x + 10.5 < 20.2 \) and write it so that \( x \) comes first, follow these steps:

1. Subtract \( 10.5 \) from both sides of the inequality:

\[ x + 10.5 - 10.5 < 20.2 - 10.5 \]

2. Simplifying this gives:

\[ x < 9.7 \]

Now, the inequality already has \( x \) first, so we can state it directly as:

\( x < 9.7 \).