Problem 128 Solve the equation for the varia... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 8: Problem 128

Solve the equation for the variable. $$c=-3 c-20$$

Short Answer

Expert verified

c = -5

Step by step solution

- Combine Like Terms

Add 3c to both sides of the equation to combine like terms involving the variable c. This gives us: \[ c + 3c = -3c + 3c - 20 \] Simplifying this results in: \[ 4c = -20 \]

- Solve for the Variable

Divide both sides of the equation by 4 to isolate c. This gives us: \[ c = \frac{-20}{4} \] Simplify the right-hand side: \[ c = -5 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Combining Like Terms

Combining like terms is a fundamental concept in algebra that helps simplify expressions and equations. Like terms are terms that have the same variable raised to the same power.
For example, in the equation given, we have $c = -3c - 20$. When we add $3c$ to both sides, we are combining the like terms involving the variable $c$. This step can be seen as:
\[ c + 3c = -3c + 3c - 20 \]
Here $c$ and $3c$ are like terms, and adding them together simplifies to \[ 4c \].
The process of combining like terms helps to reduce the complexity of the equation and makes it easier to solve for the variable.

Isolating the Variable

Isolating the variable is crucial for solving algebraic equations. The goal is to get the variable by itself on one side of the equation. After combining the like terms in our example, we have the simplified equation:
\[ 4c = -20 \]
To isolate $c$, we need to get rid of the coefficient (the number multiplying the variable).
We do this by performing the inverse operation. Here, $4c$ means $4 \times c$, so we divide both sides of the equation by 4:
\[ 4c \div 4 = -20 \div 4 \]
This simplifies to:
\[ c = -5 \]
By isolating the variable, we find that $c = -5$. This process reveals the value of the variable that satisfies the original equation.

Prealgebra Concepts

Understanding prealgebra concepts is key to mastering more complex algebraic problems. Prealgebra lays the groundwork for these skills:

Arithmetic Operations: Addition, subtraction, multiplication, and division of numbers.
Basic Equations: Understanding how to form and solve simple equations.
Like Terms: Recognizing and combining like terms.
Inverse Operations: Using operations like addition/subtraction and multiplication/division to simplify equations.

In our example, all these prealgebra concepts come into play. We combine like terms, use inverse operations, and solve the equation step-by-step. By mastering these prealgebra basics, students gain a strong foundation for tackling more advanced algebra.

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91影视

Solve the equation for the variable. $$c=-3 c-20$$

Short Answer

Step by step solution

- Combine Like Terms

- Solve for the Variable

Key Concepts

Combining Like Terms

Isolating the Variable

Prealgebra Concepts

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