Math / Algebra

QuestionAssignment Active
Analyzing a Solution
A student concluded that the solution to the equation $\sqrt{2 x+1}+3=0$ is $x=4$ .
Do you agree? Explain why or why not. $\square$ DONE

Studdy Solution

STEP 1

What is this asking? Is $x = 4$ the correct solution to the equation $\sqrt{2x + 1} + 3 = 0$ ? Watch out! Square roots can be tricky!
Remember a square root can't be negative.

STEP 2

1. Isolate the Square Root
2. Square Both Sides
3. Solve for $x$
4. Check the Solution

STEP 3

Let's isolate that square root term!
We want to get $\sqrt{2x + 1}$ all by itself on one side of the equation.
Our equation is $\sqrt{2x + 1} + 3 = 0$ .
To do this, we'll subtract $3$ from both sides of the equation.
This is like carefully removing a weight from a balanced scale – we have to do it on both sides to keep things equal!

STEP 4

Subtracting $3$ from both sides gives us: $\sqrt{2x + 1} + 3 - 3 = 0 - 3$ $\sqrt{2x + 1} = -3$ Now our square root is nicely isolated!

STEP 5

To get rid of the square root, we're going to square both sides of the equation.
Think of it like unwrapping a present – squaring a square root removes the "root" and leaves us with what's inside.

STEP 6

Squaring both sides gives us: $(\sqrt{2x + 1})^2 = (-3)^2$ $2x + 1 = 9$ Look at that, no more square roots!

STEP 7

Now, we just need to solve for $x$ .
First, let's subtract $1$ from both sides: $2x + 1 - 1 = 9 - 1$ $2x = 8$

STEP 8

Next, we'll divide both sides by $2$ to get $x$ all alone: $\frac{2x}{2} = \frac{8}{2}$ $x = 4$ So, we get $x = 4$ , just like the student did!
But wait, there's one more crucial step...

STEP 9

We always need to check our solution with square root equations.
Sometimes, we get solutions that don't actually work in the original equation.
These are called extraneous solutions.
Let's plug $x = 4$ back into the original equation: $\sqrt{2(4) + 1} + 3 = 0$ $\sqrt{8 + 1} + 3 = 0$ $\sqrt{9} + 3 = 0$ $3 + 3 = 0$ $6 = 0$ Uh oh!
That's definitely not true!

STEP 10

$x = 4$ is not the correct solution.
In fact, there's no solution to this equation!
We found that when we plugged $x = 4$ back in, we got a statement that isn't true.
This means there's no value of $x$ that will satisfy the original equation.

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QuestionAssignment Active
Analyzing a Solution
A student concluded that the solution to the equation $\sqrt{2 x+1}+3=0$ is $x=4$ .
Do you agree? Explain why or why not. $\square$ DONE

Studdy Solution

STEP 1

What is this asking? Is $x = 4$ the correct solution to the equation $\sqrt{2x + 1} + 3 = 0$ ? Watch out! Square roots can be tricky!
Remember a square root can't be negative.

STEP 2

1. Isolate the Square Root
2. Square Both Sides
3. Solve for $x$
4. Check the Solution

STEP 3

STEP 4

Subtracting $3$ from both sides gives us: $\sqrt{2x + 1} + 3 - 3 = 0 - 3$ $\sqrt{2x + 1} = -3$ Now our square root is nicely isolated!

STEP 5

To get rid of the square root, we're going to square both sides of the equation.
Think of it like unwrapping a present – squaring a square root removes the "root" and leaves us with what's inside.

STEP 6

Squaring both sides gives us: $(\sqrt{2x + 1})^2 = (-3)^2$ $2x + 1 = 9$ Look at that, no more square roots!

STEP 7

Now, we just need to solve for $x$ .
First, let's subtract $1$ from both sides: $2x + 1 - 1 = 9 - 1$ $2x = 8$

STEP 8

Next, we'll divide both sides by $2$ to get $x$ all alone: $\frac{2x}{2} = \frac{8}{2}$ $x = 4$ So, we get $x = 4$ , just like the student did!
But wait, there's one more crucial step...

STEP 9

STEP 10

$x = 4$ is not the correct solution.
In fact, there's no solution to this equation!
We found that when we plugged $x = 4$ back in, we got a statement that isn't true.
This means there's no value of $x$ that will satisfy the original equation.

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QuestionAssignment ActiveAnalyzing a SolutionA student concluded that the solution to the equation 2x+1+3=0\sqrt{2 x+1}+3=02x+1​+3=0 is x=4x=4x=4.Do you agree? Explain why or why not. □\square□ DONE

Studdy Solution

STEP 1

What is this asking? Is x=4x = 4x=4 the correct solution to the equation 2x+1+3=0\sqrt{2x + 1} + 3 = 02x+1​+3=0? Watch out! Square roots can be tricky!Remember a square root can't be negative.

STEP 2

1. Isolate the Square Root2. Square Both Sides3. Solve for xxx4. Check the Solution

STEP 3

STEP 4

Subtracting 333 from both sides gives us: 2x+1+3−3=0−3 \sqrt{2x + 1} + 3 - 3 = 0 - 3 2x+1​+3−3=0−3 2x+1=−3 \sqrt{2x + 1} = -3 2x+1​=−3Now our square root is nicely isolated!

STEP 5

To get rid of the square root, we're going to **square both sides** of the equation.Think of it like unwrapping a present – squaring a square root removes the "root" and leaves us with what's inside.

STEP 6

Squaring both sides gives us: (2x+1)2=(−3)2 (\sqrt{2x + 1})^2 = (-3)^2 (2x+1​)2=(−3)2 2x+1=9 2x + 1 = 9 2x+1=9Look at that, no more square roots!

STEP 7

Now, we just need to **solve for** xxx.First, let's **subtract** 111 from both sides: 2x+1−1=9−1 2x + 1 - 1 = 9 - 1 2x+1−1=9−1 2x=8 2x = 8 2x=8

STEP 8

Next, we'll **divide** both sides by 222 to get xxx all alone: 2x2=82 \frac{2x}{2} = \frac{8}{2} 22x​=28​ x=4 x = 4 x=4So, we get x=4x = 4x=4, just like the student did!But wait, there's one more crucial step...

STEP 9

STEP 10

x=4x = 4x=4 is *not* the correct solution.In fact, there's no solution to this equation!We found that when we plugged x=4x = 4x=4 back in, we got a statement that isn't true.This means there's no value of xxx that will satisfy the original equation.

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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.

QuestionAssignment Active
Analyzing a Solution
A student concluded that the solution to the equation $\sqrt{2 x+1}+3=0$ is $x=4$ .
Do you agree? Explain why or why not. $\square$ DONE

What is this asking? Is $x = 4$ the correct solution to the equation $\sqrt{2x + 1} + 3 = 0$ ? Watch out! Square roots can be tricky!
Remember a square root can't be negative.

1. Isolate the Square Root
2. Square Both Sides
3. Solve for $x$
4. Check the Solution

Subtracting $3$ from both sides gives us: $\sqrt{2x + 1} + 3 - 3 = 0 - 3$ $\sqrt{2x + 1} = -3$ Now our square root is nicely isolated!

To get rid of the square root, we're going to square both sides of the equation.
Think of it like unwrapping a present – squaring a square root removes the "root" and leaves us with what's inside.

Squaring both sides gives us: $(\sqrt{2x + 1})^2 = (-3)^2$ $2x + 1 = 9$ Look at that, no more square roots!

Now, we just need to solve for $x$ .
First, let's subtract $1$ from both sides: $2x + 1 - 1 = 9 - 1$ $2x = 8$

Next, we'll divide both sides by $2$ to get $x$ all alone: $\frac{2x}{2} = \frac{8}{2}$ $x = 4$ So, we get $x = 4$ , just like the student did!
But wait, there's one more crucial step...

$x = 4$ is not the correct solution.
In fact, there's no solution to this equation!
We found that when we plugged $x = 4$ back in, we got a statement that isn't true.
This means there's no value of $x$ that will satisfy the original equation.