Solved on Sep 15, 2023

Find the value of $q$ that satisfies $|q-745| = 10$ , then graph the solution on a number line.

STEP 1

Assumptions1. The absolute value of a number is its distance from zero on the number line. . The absolute value of a number is always positive or zero, but never negative.
3. The equation is in the form of $|x| = a$ , where $x$ is the expression inside the absolute value and $a$ is a positive number. The solutions to this equation are $x = a$ and $x = -a$ .

STEP 2

We need to set up two equations to solve for $q$ based on the properties of absolute value. The two equations are $q-745 =10$ and $q-745 = -10$ .

STEP 3

Let's solve the first equation $q-745 =10$ for $q$ .
$q =10 +745$

STEP 4

Calculate the value of $q$ .
$q =10 +745 =755$

STEP 5

Now, let's solve the second equation $q-745 = -10$ for $q$ .
$q = -10 +745$

STEP 6

Calculate the value of $q$ .
$q = -10 +745 =735$

STEP 7

The solutions to the equation are $q =755$ and $q =735$ .

STEP 8

To graph the solution on the number line, mark the points at $q =735$ and $q =755$ .

Was this helpful?

Find the value of $q$ that satisfies $|q-745| = 10$ , then graph the solution on a number line.

STEP 1

STEP 2

We need to set up two equations to solve for $q$ based on the properties of absolute value. The two equations are $q-745 =10$ and $q-745 = -10$ .

STEP 3

Let's solve the first equation $q-745 =10$ for $q$ .
$q =10 +745$

STEP 4

Calculate the value of $q$ .
$q =10 +745 =755$

STEP 5

Now, let's solve the second equation $q-745 = -10$ for $q$ .
$q = -10 +745$

STEP 6

Calculate the value of $q$ .
$q = -10 +745 =735$

STEP 7

The solutions to the equation are $q =755$ and $q =735$ .

STEP 8

To graph the solution on the number line, mark the points at $q =735$ and $q =755$ .

Start learning now

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

Find the value of qqq that satisfies ∣q−745∣=10|q-745| = 10∣q−745∣=10, then graph the solution on a number line.

STEP 1

STEP 2

We need to set up two equations to solve for qqq based on the properties of absolute value. The two equations are q−745=10q-745 =10q−745=10 and q−745=−10q-745 = -10q−745=−10.

STEP 3

Let's solve the first equation q−745=10q-745 =10q−745=10 for qqq.q=10+745q =10 +745q=10+745

STEP 4

Calculate the value of qqq.q=10+745=755q =10 +745 =755q=10+745=755

STEP 5

Now, let's solve the second equation q−745=−10q-745 = -10q−745=−10 for qqq.q=−10+745q = -10 +745q=−10+745

STEP 6

Calculate the value of qqq.q=−10+745=735q = -10 +745 =735q=−10+745=735

STEP 7

The solutions to the equation are q=755q =755q=755 and q=735q =735q=735.

STEP 8

To graph the solution on the number line, mark the points at q=735q =735q=735 and q=755q =755q=755.

Start learning now

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

Find the value of $q$ that satisfies $|q-745| = 10$ , then graph the solution on a number line.

We need to set up two equations to solve for $q$ based on the properties of absolute value. The two equations are $q-745 =10$ and $q-745 = -10$ .

Let's solve the first equation $q-745 =10$ for $q$ .
$q =10 +745$

Calculate the value of $q$ .
$q =10 +745 =755$

Now, let's solve the second equation $q-745 = -10$ for $q$ .
$q = -10 +745$

Calculate the value of $q$ .
$q = -10 +745 =735$

The solutions to the equation are $q =755$ and $q =735$ .

To graph the solution on the number line, mark the points at $q =735$ and $q =755$ .