To solve for \( c \) in the equation \( 3ab - 2bc = 12 \), follow these steps:

### Step 1: Isolate the term with \( c \)
We want to move all terms involving \( c \) to one side. Start by subtracting \( 3ab \) from both sides of the equation:

\[
-2bc = 12 - 3ab
\]

### Step 2: Solve for \( c \)
Now, divide both sides of the equation by \( -2b \) to isolate \( c \):

\[
c = \frac{12 - 3ab}{-2b}
\]

### Step 3: Simplify the expression
You can simplify the fraction by factoring out the negative sign:

\[
c = \frac{-(12 - 3ab)}{2b}
\]

or

\[
c = \frac{3ab - 12}{2b}
\]

This is the solution for \( c \).

Would you like further details or have any questions?

Here are 5 related questions to practice:

1. Solve \( 4xy - 5yz = 20 \) for \( z \).
2. Solve \( 2ab - 3ac = 15 \) for \( c \).
3. If \( 3ab - 2bc = 0 \), solve for \( c \).
4. Solve \( 6xy + 2yz = 10 \) for \( z \).
5. Solve \( 5ac + 7bc = 25 \) for \( c \).

**Tip:** When solving for a variable, always aim to isolate that variable on one side of the equation by using inverse operations (e.g., addition, subtraction, multiplication, division).

Learn how to solve the linear equation 3ab - 2bc = 12 for c with a step-by-step guide. This problem covers key algebraic concepts and demonstrates isolating variables using basic algebraic operations. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation