To solve the equation \(2x = 20\), we first divide both sides by 2:
\[ x = \frac{20}{2} = 10 \]
The solution to the equation is \(x = 10\).
In set notation, we express this solution as:
\[ {10} \]
11 answers
To solve the equation \(2x = 20\), we first divide both sides by 2:
\[ x = \frac{20}{2} = 10 \]
The solution to the equation is \(x = 10\).
In set notation, we express this solution as:
\[ {10} \]
To solve the equation \(\frac{x^2}{2} = 18\), we first multiply both sides by 2:
\[ x^2 = 36 \]
Next, we take the square root of both sides:
\[ x = 6 \quad \text{or} \quad x = -6 \]
The solutions to the equation are \(6\) and \(-6\).
In set notation, listing the elements in order from least to greatest, we express this as:
\[ {-6, 6} \]
To express the solution to the inequality \(4y + 1 > 17\) in set notation, we first solve for \(y\):
Subtract 1 from both sides: \[ 4y > 16 \]
Divide both sides by 4: \[ y > 4 \]
The solution to the inequality is \(y > 4\).
In set notation, this is expressed as:
\[ (4, \infty) \]
This interval notation indicates that \(y\) can take any value greater than 4.
I apologize for any confusion in my previous response. In set notation, the values of \(y\) that satisfy the inequality \(4y + 1 > 17\), which simplifies to \(y > 4\), can be expressed as follows:
\[ { y \in \mathbb{R} \mid y > 4 } \]
This notation means "the set of all real numbers \(y\) such that \(y\) is greater than 4."
If you prefer interval notation (which is also a standard way to represent ranges), the solution is:
\[ (4, \infty) \]
However, since you requested set notation specifically, the first representation is the correct answer. Thank you for your understanding!
To determine which person is correct, we first need to solve the compound inequality \(-2 \leq 2x - 2 < 8\).
We'll break it down into two parts:
Solving the left part: \(-2 \leq 2x - 2\)
Add 2 to both sides: \[ 0 \leq 2x \] Divide by 2: \[ 0 \leq x \quad \text{or} \quad x \geq 0 \]
Solving the right part: \(2x - 2 < 8\)
Add 2 to both sides: \[ 2x < 10 \] Divide by 2: \[ x < 5 \]
Combining both parts, we have: \[ 0 \leq x < 5 \]
Now we evaluate who among Sophie, Adola, and Gilly is correct:
Thus, Gilly is correct. The correct answer is:
3
To solve the inequality \(2m < 14\), we first divide both sides by 2:
\[ m < 7 \]
Now, let's evaluate the provided options for correct set notation that describes the values of \(m\) making the inequality true:
Option #1: \({m: m < 7}\) - This option correctly indicates that \(m\) is any value less than 7. This is the correct set notation.
Option #2: \({7: 7 < m}\) - This option incorrectly suggests that the set contains \(7\) as an element, which is not correct since \(m\) should be less than \(7\).
Option #3: \({m < 7: m}\) - This option is incorrect and does not represent valid set notation.
Option #4: \({m < 7}\) - This option also does not represent values in correct set notation since it does not involve a relationship or a proper statement for \(m\).
Based on this analysis, Option #1: \({m: m < 7}\) is the correct choice.