true. Enter your response using set notation.(1 point)
7 answers
To solve the equation \(2x = 20\), we first isolate \(x\) by dividing both sides by 2:
\[ x = \frac{20}{2} = 10 \]
The solution to the equation is \(x = 10\).
In set notation, we can express this as:
\[ {10} \]
Thus, the set of values that make the equation true is \({10}\).
To express the solutions \(-6\) and \(6\) in set notation, we list them from least to greatest.
Thus, the set notation for the solutions is:
\[ {-6, 6} \]
To express the solution to the inequality \(4y + 1 > 17\) in set notation, we first note that the solution is \(y > 4\).
In set notation, this can be expressed as:
\[ { y , | , y > 4 } \]
Alternatively, if we are considering the interval form, we could write:
\[ (4, \infty) \]
But the most straightforward set notation representation is :
\[ { y , | , y > 4 } \]
This indicates the set of all \(y\) such that \(y\) is greater than 4.
To determine which person is correct regarding the solutions to the compound inequality \(-2 \leq 2x - 2 < 8\), we will solve the compound inequality step by step.
Solve the left part of the inequality: \[ -2 \leq 2x - 2 \] Add 2 to both sides: \[ 0 \leq 2x \] Divide both sides by 2: \[ 0 \leq x \quad \text{or} \quad x \geq 0 \]
Solve the right part of the inequality: \[ 2x - 2 < 8 \] Add 2 to both sides: \[ 2x < 10 \] Divide both sides by 2: \[ x < 5 \]
Combine the results: The solution set to the compound inequality is: \[ 0 \leq x < 5 \] This means \(x\) can take any value starting from \(0\) (inclusive) up to \(5\) (but not including \(5\)).
Next, we check each person's claim:
Sophie says that \(-2\) is a solution. \(-2\) is not in the interval \([0, 5)\).
Adola says that \(5\) is a solution. \(5\) is not included in the interval \([0, 5)\).
Gilly says that \(2\) is a solution. \(2\) is within the interval \([0, 5)\).
Since Gilly's claim that \(2\) is a solution is correct, the answer is:
The person who is correct is person 3.
