Problem 40 Solve each equation. $$8 c-7(c... [FREE SOLUTION]

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Chapter 2: Problem 40

Solve each equation. $$8 c-7(c-3)+4=-16$$

Short Answer

Expert verified

c = -41

Step by step solution

Distribute and Simplify

Distribute the -7 through the parenthesis: 8c - 7c + 21 + 4 = -16

Combine Like Terms

Combine the like terms on the left side of the equation: c + 25 = -16

Isolate the Variable

Subtract 25 from both sides of the equation to solve for c: c = -41

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Key Concepts

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

Distributive Property

When we see an expression like $8c - 7(c - 3) + 4$, we need to use the distributive property. This property allows us to multiply each term inside the parentheses by the number outside. \[ -7(c - 3) \].

Here's how it works:

Multiply \-7\ by $c$. That gives us $-7c$.
Next, multiply \-7\ by \-3\. This results in $21$ because two negatives make a positive.

So, we rewrite the expression: \[8c - 7c + 21 + 4\].
Using the distributive property simplifies complex expressions and helps us move closer to solving the equation!

Combining Like Terms

After using the distributive property, our equation is now $8c - 7c + 21 + 4 = -16$.

The next step is to combine like terms. Like terms are terms that have the same variable raised to the same power.

The terms \8c\ and \-7c\ are like terms because they both contain the variable $c$.
Combine these to get $c$. So, \[8c - 7c = c\].
Next, combine the constant terms $21$ and $4$ to get $25$. These are constants because they don't contain a variable.

So now, our simplified equation is $c + 25 = -16$.
Combining like terms makes the equation simpler and easier to solve.

Isolating the Variable

Finally, we need to isolate the variable $c$ to solve for it.

Our simplified equation is $c + 25 = -16$. To isolate the variable, we perform operations that will leave $c$ alone on one side of the equation.

Subtract $25$ from both sides of the equation to keep it balanced. So, \[c + 25 - 25 = -16 - 25\].
This simplifies to \[c = -41\].

Isolating the variable means getting $c$ by itself. Now we know that $c=-41$. Always check your solution by plugging it back into the original equation to ensure it's correct.
Understanding these steps helps you tackle any linear equation confidently.

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91影视

Solve each equation. $$8 c-7(c-3)+4=-16$$

Short Answer

Step by step solution

Distribute and Simplify

Combine Like Terms

Isolate the Variable

Key Concepts

Distributive Property

Combining Like Terms

Isolating the Variable

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