Asked by Monkey balls
which value of y will make the equation true?
-5y+3=-(3y-9)
-1/3
-3
3
All real numbers
-5y+3=-(3y-9)
-1/3
-3
3
All real numbers
Answers
Answered by
Monkey balls
what does having a closed circle on a number line mean?
Answered by
Monkey balls
does closed circle on a number line mean ≤ or <
Answered by
Monkey balls
would x<3 have an open circle?
Answered by
Monkey balls
solve the inequality 3x-5≥13
Answered by
Monkey balls
how many solutions does this have. 2(2m+3)-6=4m
Answered by
GPT-4o mini
To solve the equation \(-5y + 3 = -(3y - 9)\), we first simplify the right side:
\[
-(3y - 9) = -3y + 9
\]
Now the equation becomes:
\[
-5y + 3 = -3y + 9
\]
Next, we'll move all terms involving \(y\) to one side and constant terms to the other side. We can add \(5y\) to both sides:
\[
3 = 2y + 9
\]
Then, subtract \(9\) from both sides:
\[
3 - 9 = 2y
\]
This simplifies to:
\[
-6 = 2y
\]
Now, divide both sides by \(2\):
\[
y = -3
\]
Thus, the value of \(y\) that makes the equation true is:
\(-3\)
\[
-(3y - 9) = -3y + 9
\]
Now the equation becomes:
\[
-5y + 3 = -3y + 9
\]
Next, we'll move all terms involving \(y\) to one side and constant terms to the other side. We can add \(5y\) to both sides:
\[
3 = 2y + 9
\]
Then, subtract \(9\) from both sides:
\[
3 - 9 = 2y
\]
This simplifies to:
\[
-6 = 2y
\]
Now, divide both sides by \(2\):
\[
y = -3
\]
Thus, the value of \(y\) that makes the equation true is:
\(-3\)
Answered by
GPT-4o mini
On a number line, a closed circle represents that the endpoint is included in the inequality or interval. This is typically used to indicate that values at that point are part of a solution set.
For example:
- In the case of an inequality like \(x \leq 3\), a closed circle on the number \(3\) means that \(3\) itself is included in the set of solutions, so all numbers less than or equal to \(3\) satisfy the inequality.
- Similarly, for intervals, a closed interval notation like \([a, b]\) means that both endpoints \(a\) and \(b\) are included in the interval.
In contrast, an open circle would indicate that the endpoint is not included in the solution set.
For example:
- In the case of an inequality like \(x \leq 3\), a closed circle on the number \(3\) means that \(3\) itself is included in the set of solutions, so all numbers less than or equal to \(3\) satisfy the inequality.
- Similarly, for intervals, a closed interval notation like \([a, b]\) means that both endpoints \(a\) and \(b\) are included in the interval.
In contrast, an open circle would indicate that the endpoint is not included in the solution set.
Answered by
GPT-4o mini
A closed circle on a number line indicates that the endpoint is included in the interval or solution set, which corresponds to the symbols \( \leq \) (less than or equal to) or \( \geq \) (greater than or equal to).
For example:
- A closed circle at \(3\) with the inequality \(x \leq 3\) indicates that \(3\) is included in the set of solutions.
- Similarly, if the inequality is \(x \geq 3\), a closed circle at \(3\) also means \(3\) is included.
In contrast, an open circle would signify the use of \( < \) (less than) or \( > \) (greater than), meaning the value at that point is not included in the set of solutions.
For example:
- A closed circle at \(3\) with the inequality \(x \leq 3\) indicates that \(3\) is included in the set of solutions.
- Similarly, if the inequality is \(x \geq 3\), a closed circle at \(3\) also means \(3\) is included.
In contrast, an open circle would signify the use of \( < \) (less than) or \( > \) (greater than), meaning the value at that point is not included in the set of solutions.
Answered by
GPT-4o mini
Yes, the inequality \( x < 3 \) would have an open circle at \( 3 \) on a number line. This indicates that \( 3 \) is not included in the set of solutions.
When graphing \( x < 3 \):
- You would place an open circle at \( 3 \) to signify that values less than \( 3 \) are included, but \( 3 \) itself is not part of the solution.
- The line would then extend to the left, including all numbers less than \( 3 \).
When graphing \( x < 3 \):
- You would place an open circle at \( 3 \) to signify that values less than \( 3 \) are included, but \( 3 \) itself is not part of the solution.
- The line would then extend to the left, including all numbers less than \( 3 \).
Answered by
GPT-4o mini
To solve the inequality \(3x - 5 \geq 13\), follow these steps:
1. **Add 5 to both sides**:
\[
3x - 5 + 5 \geq 13 + 5
\]
\[
3x \geq 18
\]
2. **Divide both sides by 3**:
\[
\frac{3x}{3} \geq \frac{18}{3}
\]
\[
x \geq 6
\]
Thus, the solution to the inequality \(3x - 5 \geq 13\) is:
\[
x \geq 6
\]
In interval notation, this is expressed as:
\[
[6, \infty)
\]
1. **Add 5 to both sides**:
\[
3x - 5 + 5 \geq 13 + 5
\]
\[
3x \geq 18
\]
2. **Divide both sides by 3**:
\[
\frac{3x}{3} \geq \frac{18}{3}
\]
\[
x \geq 6
\]
Thus, the solution to the inequality \(3x - 5 \geq 13\) is:
\[
x \geq 6
\]
In interval notation, this is expressed as:
\[
[6, \infty)
\]
Answered by
GPT-4o mini
To determine the number of solutions for the equation \(2(2m + 3) - 6 = 4m\), we can start by simplifying it step by step.
1. Distribute the \(2\) on the left side:
\[
4m + 6 - 6 = 4m
\]
This simplifies to:
\[
4m = 4m
\]
2. Now, we see that \(4m\) on the left side is equal to \(4m\) on the right side. This implies that the equation is true for all values of \(m\).
Since the equation simplifies to a true statement (\(4m = 4m\)) without any restrictions on \(m\), it indicates that there are **infinitely many solutions**.
Thus, the final answer is that the equation has **infinitely many solutions**.
1. Distribute the \(2\) on the left side:
\[
4m + 6 - 6 = 4m
\]
This simplifies to:
\[
4m = 4m
\]
2. Now, we see that \(4m\) on the left side is equal to \(4m\) on the right side. This implies that the equation is true for all values of \(m\).
Since the equation simplifies to a true statement (\(4m = 4m\)) without any restrictions on \(m\), it indicates that there are **infinitely many solutions**.
Thus, the final answer is that the equation has **infinitely many solutions**.