Math / Algebra

Questionmylab.pearson.com Quanto Griffin ebra - FL 2024 HW Score: $62.9 \%, 19.5$ of 31 points : HW Units 1.4 \& 1.6 1.6 .45 Points: 0 of 1 Save
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Solve. $4|q|-3=6$ A. The solution set is $\square$ \}. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. The solution set is the empty set.

Studdy Solution

STEP 1

What is this asking? We need to find the values of $q$ that make the equation $4|q| - 3 = 6$ true. Watch out! Absolute values can be tricky!
Remember that $|q|$ is the distance of $q$ from zero, so it's always non-negative.
This means we might get two answers!

STEP 2

1. Isolate the absolute value
2. Split into two equations
3. Solve for q

STEP 3

We want to get $|q|$ by itself.
The equation is $4|q| - 3 = 6$ .
Let's add 3 to both sides to get rid of the -3 on the left.
This gives us $4|q| - 3 + 3 = 6 + 3$ , which simplifies to $4|q| = 9$ .
Why did we do this?
Because we want to isolate the absolute value of $q$ !

STEP 4

Now, we have $4|q| = 9$ .
To completely isolate $|q|$ , we divide both sides by 4.
This gives us $\frac{4|q|}{4} = \frac{9}{4}$ , which simplifies to $|q| = \frac{9}{4}$ .
Awesome!

STEP 5

Remember, the absolute value of a number is its distance from zero.
So, if $|q| = \frac{9}{4}$ , then $q$ could be $\frac{9}{4}$ or $-\frac{9}{4}$ because both numbers are $\frac{9}{4}$ units away from zero.

STEP 6

This gives us two equations to solve: $q = \frac{9}{4}$ and $q = -\frac{9}{4}$ .

STEP 7

Look at that, our equations from the previous step, $q = \frac{9}{4}$ and $q = -\frac{9}{4}$ , are already solved for $q$ !
We have our two solutions!

STEP 8

The solution set is $\{-\frac{9}{4}, \frac{9}{4}\}$ .
So, the answer is A, with $-\frac{9}{4}$ and $\frac{9}{4}$ in the box.

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Studdy Solution

STEP 1

What is this asking? We need to find the values of $q$ that make the equation $4|q| - 3 = 6$ true. Watch out! Absolute values can be tricky!
Remember that $|q|$ is the distance of $q$ from zero, so it's always non-negative.
This means we might get two answers!

STEP 2

1. Isolate the absolute value
2. Split into two equations
3. Solve for q

STEP 3

We want to get $|q|$ by itself.
The equation is $4|q| - 3 = 6$ .
Let's add 3 to both sides to get rid of the -3 on the left.
This gives us $4|q| - 3 + 3 = 6 + 3$ , which simplifies to $4|q| = 9$ .
Why did we do this?
Because we want to isolate the absolute value of $q$ !

STEP 4

Now, we have $4|q| = 9$ .
To completely isolate $|q|$ , we divide both sides by 4.
This gives us $\frac{4|q|}{4} = \frac{9}{4}$ , which simplifies to $|q| = \frac{9}{4}$ .
Awesome!

STEP 5

Remember, the absolute value of a number is its distance from zero.
So, if $|q| = \frac{9}{4}$ , then $q$ could be $\frac{9}{4}$ or $-\frac{9}{4}$ because both numbers are $\frac{9}{4}$ units away from zero.

STEP 6

This gives us two equations to solve: $q = \frac{9}{4}$ and $q = -\frac{9}{4}$ .

STEP 7

Look at that, our equations from the previous step, $q = \frac{9}{4}$ and $q = -\frac{9}{4}$ , are already solved for $q$ !
We have our two solutions!

STEP 8

The solution set is $\{-\frac{9}{4}, \frac{9}{4}\}$ .
So, the answer is A, with $-\frac{9}{4}$ and $\frac{9}{4}$ in the box.

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Studdy Solution

STEP 1

What is this asking? We need to find the values of qqq that make the equation 4∣q∣−3=64|q| - 3 = 64∣q∣−3=6 true. Watch out! Absolute values can be tricky!Remember that ∣q∣|q|∣q∣ is the distance of qqq from zero, so it's always non-negative.This means we might get two answers!

STEP 2

1. Isolate the absolute value2. Split into two equations3. Solve for *q*

STEP 3

STEP 4

Now, we have 4∣q∣=94|q| = 94∣q∣=9.To completely isolate ∣q∣|q|∣q∣, we divide both sides by **4**.This gives us 4∣q∣4=94\frac{4|q|}{4} = \frac{9}{4}44∣q∣​=49​, which simplifies to ∣q∣=94|q| = \frac{9}{4}∣q∣=49​.Awesome!

STEP 5

Remember, the absolute value of a number is its distance from zero.So, if ∣q∣=94|q| = \frac{9}{4}∣q∣=49​, then qqq could be 94\frac{9}{4}49​ or −94-\frac{9}{4}−49​ because both numbers are 94\frac{9}{4}49​ units away from zero.

STEP 6

This gives us two equations to solve: q=94q = \frac{9}{4}q=49​ and q=−94q = -\frac{9}{4}q=−49​.

STEP 7

Look at that, our equations from the previous step, q=94q = \frac{9}{4}q=49​ and q=−94q = -\frac{9}{4}q=−49​, are already solved for qqq!We have our two solutions!

STEP 8

The solution set is {−94,94}\{-\frac{9}{4}, \frac{9}{4}\}{−49​,49​}.So, the answer is A, with −94-\frac{9}{4}−49​ and 94\frac{9}{4}49​ in the box.

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.

What is this asking? We need to find the values of $q$ that make the equation $4|q| - 3 = 6$ true. Watch out! Absolute values can be tricky!
Remember that $|q|$ is the distance of $q$ from zero, so it's always non-negative.
This means we might get two answers!

1. Isolate the absolute value
2. Split into two equations
3. Solve for q

Now, we have $4|q| = 9$ .
To completely isolate $|q|$ , we divide both sides by 4.
This gives us $\frac{4|q|}{4} = \frac{9}{4}$ , which simplifies to $|q| = \frac{9}{4}$ .
Awesome!

Remember, the absolute value of a number is its distance from zero.
So, if $|q| = \frac{9}{4}$ , then $q$ could be $\frac{9}{4}$ or $-\frac{9}{4}$ because both numbers are $\frac{9}{4}$ units away from zero.

This gives us two equations to solve: $q = \frac{9}{4}$ and $q = -\frac{9}{4}$ .

Look at that, our equations from the previous step, $q = \frac{9}{4}$ and $q = -\frac{9}{4}$ , are already solved for $q$ !
We have our two solutions!

The solution set is $\{-\frac{9}{4}, \frac{9}{4}\}$ .
So, the answer is A, with $-\frac{9}{4}$ and $\frac{9}{4}$ in the box.