Use set notation to express the value(s) that make the equation 2x=20

Question

true. Enter your response using set notation.(1 point)

Answer 1

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 $10$.

Answer 2

Both −6
and 6 make the equation x22=18
true. Use set notation to express these solutions. When entering your response, list elements in the set from least to greatest, with a comma between each element in the set.(1 point)

Answer 3

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:

$$-6,6$$

Answer 4

The solution to the inequality 4y+1>17
is y>4
. Use set notation to express the values of y that make the inequality 4y+1>17
true.(1 point)

Answer 5

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:

$$(4,\mathrm{\infty })$$

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.

Answer 6

Sophie, Adola, and Gilly are debating potential values in the solution set of the compound inequality −2≤2x−2<8
. Sophie says that −2
is a solution. Adola says that 5 is a solution. Gilly says that 2 is a solution. Which person is correct? Enter 1 for Sophie, 2 for Adola, or 3 for Gilly.(1 point)
The person who is correct is person

Answer 7

To determine which person is correct regarding the solutions to the compound inequality $-2\le 2x-2<8$, we will solve the compound inequality step by step.

1. Solve the left part of the inequality: $$-2\le 2x-2$$ Add 2 to both sides: $$0\le 2x$$ Divide both sides by 2: $$0\le x\text{or}x\ge 0$$

2. Solve the right part of the inequality: $$2x-2<8$$ Add 2 to both sides: $$2x<10$$ Divide both sides by 2: $$x<5$$

3. Combine the results: The solution set to the compound inequality is: $$0\le x<5$$ 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.