Math / Algebra

Question5. Which of the following values of $x$ does not lie in the domain of $y=-2 \sqrt{5-2 x}$ ? (1) -3 (3) 2.5 (2) 2 (4) 4
COMMON CORE Algebra II, Final ASSESSMENTS (1)

Studdy Solution

STEP 1

What is this asking? Which of these $x$ values makes the stuff inside the square root negative? Watch out! Remember, we can't take the square root of a negative number!

STEP 2

1. Set up the inequality
2. Solve the inequality

STEP 3

Alright, so we've got this square root, and we know the stuff inside can't be negative.
That means it has to be greater than or equal to zero!
So, let's write that down as an inequality: $5 - 2x \ge 0$

STEP 4

Let's isolate our $x$ term.
We can do this by subtracting 5 from both sides of the inequality: $5 - 2x - 5 \ge 0 - 5$ $-2x \ge -5$

STEP 5

Now, we need to get $\bf x$ by itself.
We'll divide both sides by -2.
But remember, when we divide or multiply an inequality by a negative number, we have to flip the inequality sign!
So: $\frac{-2x}{-2} \le \frac{-5}{-2}$ $x \le \frac{5}{2}$

STEP 6

We know that $\frac{5}{2}$ is the same as 2.5, so: $x \le 2.5$

STEP 7

This tells us that $x$ can be any number less than or equal to 2.5.
Let's check our options: $x = -3$ is less than 2.5. $x = 2$ is less than 2.5. $x = 2.5$ is equal to 2.5. $x = 4$ is greater than 2.5.

STEP 8

Since $x$ must be less than or equal to 2.5, the value $x = 4$ does not lie in the domain of the function.
So the answer is (4).

Was this helpful?

Question5. Which of the following values of $x$ does not lie in the domain of $y=-2 \sqrt{5-2 x}$ ? (1) -3 (3) 2.5 (2) 2 (4) 4
COMMON CORE Algebra II, Final ASSESSMENTS (1)

Studdy Solution

STEP 1

What is this asking? Which of these $x$ values makes the stuff inside the square root negative? Watch out! Remember, we can't take the square root of a negative number!

STEP 2

1. Set up the inequality
2. Solve the inequality

STEP 3

Alright, so we've got this square root, and we know the stuff inside can't be negative.
That means it has to be greater than or equal to zero!
So, let's write that down as an inequality: $5 - 2x \ge 0$

STEP 4

Let's isolate our $x$ term.
We can do this by subtracting 5 from both sides of the inequality: $5 - 2x - 5 \ge 0 - 5$ $-2x \ge -5$

STEP 5

Now, we need to get $\bf x$ by itself.
We'll divide both sides by -2.
But remember, when we divide or multiply an inequality by a negative number, we have to flip the inequality sign!
So: $\frac{-2x}{-2} \le \frac{-5}{-2}$ $x \le \frac{5}{2}$

STEP 6

We know that $\frac{5}{2}$ is the same as 2.5, so: $x \le 2.5$

STEP 7

This tells us that $x$ can be any number less than or equal to 2.5.
Let's check our options: $x = -3$ is less than 2.5. $x = 2$ is less than 2.5. $x = 2.5$ is equal to 2.5. $x = 4$ is greater than 2.5.

STEP 8

Since $x$ must be less than or equal to 2.5, the value $x = 4$ does not lie in the domain of the function.
So the answer is (4).

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question5. Which of the following values of xxx does not lie in the domain of y=−25−2xy=-2 \sqrt{5-2 x}y=−25−2x​ ? (1) -3 (3) 2.5 (2) 2 (4) 4COMMON CORE Algebra II, Final ASSESSMENTS (1)

Studdy Solution

STEP 1

What is this asking? Which of these xxx values makes the stuff inside the square root negative? Watch out! Remember, we can't take the square root of a negative number!

STEP 2

1. Set up the inequality2. Solve the inequality

STEP 3

Alright, so we've got this square root, and we know the stuff inside can't be negative.That means it has to be greater than or equal to zero!So, let's **write that down** as an inequality: 5−2x≥05 - 2x \ge 05−2x≥0

STEP 4

Let's **isolate** our xxx term.We can do this by subtracting 5 from both sides of the inequality: 5−2x−5≥0−55 - 2x - 5 \ge 0 - 55−2x−5≥0−5 −2x≥−5-2x \ge -5−2x≥−5

STEP 5

STEP 6

We know that 52\frac{5}{2}25​ is the same as **2.5**, so: x≤2.5x \le 2.5x≤2.5

STEP 7

This tells us that xxx can be any number less than or equal to 2.5.Let's **check our options**: x=−3x = -3x=−3 is less than 2.5. x=2x = 2x=2 is less than 2.5. x=2.5x = 2.5x=2.5 is equal to 2.5. x=4x = 4x=4 is *greater* than 2.5.

STEP 8

Since xxx must be less than or equal to 2.5, the value x=4x = 4x=4 does *not* lie in the domain of the function.So the answer is (4).

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question5. Which of the following values of $x$ does not lie in the domain of $y=-2 \sqrt{5-2 x}$ ? (1) -3 (3) 2.5 (2) 2 (4) 4
COMMON CORE Algebra II, Final ASSESSMENTS (1)

What is this asking? Which of these $x$ values makes the stuff inside the square root negative? Watch out! Remember, we can't take the square root of a negative number!

1. Set up the inequality
2. Solve the inequality

Alright, so we've got this square root, and we know the stuff inside can't be negative.
That means it has to be greater than or equal to zero!
So, let's write that down as an inequality: $5 - 2x \ge 0$

Let's isolate our $x$ term.
We can do this by subtracting 5 from both sides of the inequality: $5 - 2x - 5 \ge 0 - 5$ $-2x \ge -5$

We know that $\frac{5}{2}$ is the same as 2.5, so: $x \le 2.5$

This tells us that $x$ can be any number less than or equal to 2.5.
Let's check our options: $x = -3$ is less than 2.5. $x = 2$ is less than 2.5. $x = 2.5$ is equal to 2.5. $x = 4$ is greater than 2.5.

Since $x$ must be less than or equal to 2.5, the value $x = 4$ does not lie in the domain of the function.
So the answer is (4).