Solved on Dec 18, 2023

Solve the absolute value equation $|5c-18|=30$ for the value of $c$ .

STEP 1

Assumptions
1. We are given the absolute value equation $|5c - 18| = 30$ .
2. We need to solve for the variable $c$ .

STEP 2

Understand that the absolute value of a number is the distance of that number from zero on the number line, which is always non-negative.

STEP 3

Recognize that the equation $|5c - 18| = 30$ means that the expression $5c - 18$ is 30 units away from zero on the number line. This can happen in two scenarios: either $5c - 18 = 30$ or $5c - 18 = -30$ .

STEP 4

First, we will solve the equation when the expression inside the absolute value is positive.
$5c - 18 = 30$

STEP 5

Add 18 to both sides of the equation to isolate the term with the variable $c$ on one side.
$5c - 18 + 18 = 30 + 18$

STEP 6

Simplify both sides of the equation.
$5c = 48$

STEP 7

Divide both sides of the equation by 5 to solve for $c$ .
$\frac{5c}{5} = \frac{48}{5}$

STEP 8

Calculate the value of $c$ .
$c = \frac{48}{5}$

STEP 9

Simplify the fraction to get the first solution for $c$ .
$c = 9.6$

STEP 10

Now, we will solve the equation when the expression inside the absolute value is negative.
$5c - 18 = -30$

STEP 11

Add 18 to both sides of the equation to isolate the term with the variable $c$ on one side.
$5c - 18 + 18 = -30 + 18$

STEP 12

Simplify both sides of the equation.
$5c = -12$

STEP 13

Divide both sides of the equation by 5 to solve for $c$ .
$\frac{5c}{5} = \frac{-12}{5}$

STEP 14

Calculate the value of $c$ .
$c = \frac{-12}{5}$

STEP 15

Simplify the fraction to get the second solution for $c$ .
$c = -2.4$
The solutions to the equation $|5c - 18| = 30$ are $c = 9.6$ and $c = -2.4$ .

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Solve the absolute value equation $|5c-18|=30$ for the value of $c$ .

STEP 1

Assumptions
1. We are given the absolute value equation $|5c - 18| = 30$ .
2. We need to solve for the variable $c$ .

STEP 2

Understand that the absolute value of a number is the distance of that number from zero on the number line, which is always non-negative.

STEP 3

Recognize that the equation $|5c - 18| = 30$ means that the expression $5c - 18$ is 30 units away from zero on the number line. This can happen in two scenarios: either $5c - 18 = 30$ or $5c - 18 = -30$ .

STEP 4

First, we will solve the equation when the expression inside the absolute value is positive.
$5c - 18 = 30$

STEP 5

Add 18 to both sides of the equation to isolate the term with the variable $c$ on one side.
$5c - 18 + 18 = 30 + 18$

STEP 6

Simplify both sides of the equation.
$5c = 48$

STEP 7

Divide both sides of the equation by 5 to solve for $c$ .
$\frac{5c}{5} = \frac{48}{5}$

STEP 8

Calculate the value of $c$ .
$c = \frac{48}{5}$

STEP 9

Simplify the fraction to get the first solution for $c$ .
$c = 9.6$

STEP 10

Now, we will solve the equation when the expression inside the absolute value is negative.
$5c - 18 = -30$

STEP 11

Add 18 to both sides of the equation to isolate the term with the variable $c$ on one side.
$5c - 18 + 18 = -30 + 18$

STEP 12

Simplify both sides of the equation.
$5c = -12$

STEP 13

Divide both sides of the equation by 5 to solve for $c$ .
$\frac{5c}{5} = \frac{-12}{5}$

STEP 14

Calculate the value of $c$ .
$c = \frac{-12}{5}$

STEP 15

Simplify the fraction to get the second solution for $c$ .
$c = -2.4$
The solutions to the equation $|5c - 18| = 30$ are $c = 9.6$ and $c = -2.4$ .

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Solve the absolute value equation ∣5c−18∣=30|5c-18|=30∣5c−18∣=30 for the value of ccc.

STEP 1

Assumptions1. We are given the absolute value equation ∣5c−18∣=30|5c - 18| = 30∣5c−18∣=30.2. We need to solve for the variable ccc.

STEP 2

Understand that the absolute value of a number is the distance of that number from zero on the number line, which is always non-negative.

STEP 3

Recognize that the equation ∣5c−18∣=30|5c - 18| = 30∣5c−18∣=30 means that the expression 5c−185c - 185c−18 is 30 units away from zero on the number line. This can happen in two scenarios: either 5c−18=305c - 18 = 305c−18=30 or 5c−18=−305c - 18 = -305c−18=−30.

STEP 4

First, we will solve the equation when the expression inside the absolute value is positive.5c−18=305c - 18 = 305c−18=30

STEP 5

Add 18 to both sides of the equation to isolate the term with the variable ccc on one side.5c−18+18=30+185c - 18 + 18 = 30 + 185c−18+18=30+18

STEP 6

Simplify both sides of the equation.5c=485c = 485c=48

STEP 7

Divide both sides of the equation by 5 to solve for ccc.5c5=485\frac{5c}{5} = \frac{48}{5}55c​=548​

STEP 8

Calculate the value of ccc.c=485c = \frac{48}{5}c=548​

STEP 9

Simplify the fraction to get the first solution for ccc.c=9.6c = 9.6c=9.6

STEP 10

Now, we will solve the equation when the expression inside the absolute value is negative.5c−18=−305c - 18 = -305c−18=−30

STEP 11

Add 18 to both sides of the equation to isolate the term with the variable ccc on one side.5c−18+18=−30+185c - 18 + 18 = -30 + 185c−18+18=−30+18

STEP 12

Simplify both sides of the equation.5c=−125c = -125c=−12

STEP 13

Divide both sides of the equation by 5 to solve for ccc.5c5=−125\frac{5c}{5} = \frac{-12}{5}55c​=5−12​

STEP 14

Calculate the value of ccc.c=−125c = \frac{-12}{5}c=5−12​

STEP 15

Simplify the fraction to get the second solution for ccc.c=−2.4c = -2.4c=−2.4The solutions to the equation ∣5c−18∣=30|5c - 18| = 30∣5c−18∣=30 are c=9.6c = 9.6c=9.6 and c=−2.4c = -2.4c=−2.4.

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

Solve the absolute value equation $|5c-18|=30$ for the value of $c$ .

Assumptions
1. We are given the absolute value equation $|5c - 18| = 30$ .
2. We need to solve for the variable $c$ .

Recognize that the equation $|5c - 18| = 30$ means that the expression $5c - 18$ is 30 units away from zero on the number line. This can happen in two scenarios: either $5c - 18 = 30$ or $5c - 18 = -30$ .

First, we will solve the equation when the expression inside the absolute value is positive.
$5c - 18 = 30$

Add 18 to both sides of the equation to isolate the term with the variable $c$ on one side.
$5c - 18 + 18 = 30 + 18$

Simplify both sides of the equation.
$5c = 48$

Divide both sides of the equation by 5 to solve for $c$ .
$\frac{5c}{5} = \frac{48}{5}$

Calculate the value of $c$ .
$c = \frac{48}{5}$

Simplify the fraction to get the first solution for $c$ .
$c = 9.6$

Now, we will solve the equation when the expression inside the absolute value is negative.
$5c - 18 = -30$

Add 18 to both sides of the equation to isolate the term with the variable $c$ on one side.
$5c - 18 + 18 = -30 + 18$

Simplify both sides of the equation.
$5c = -12$

Divide both sides of the equation by 5 to solve for $c$ .
$\frac{5c}{5} = \frac{-12}{5}$

Calculate the value of $c$ .
$c = \frac{-12}{5}$

Simplify the fraction to get the second solution for $c$ .
$c = -2.4$
The solutions to the equation $|5c - 18| = 30$ are $c = 9.6$ and $c = -2.4$ .