Problem 13 Solve the equation. $$8 c-12=3... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 3: Problem 13

Solve the equation. $$8 c-12=36$$

Short Answer

Expert verified

c = 6

Step by step solution

- Add 12 to both sides

To isolate the term with the variable, add 12 to both sides of the equation.$8c - 12 + 12 = 36 + 12$This simplifies to:$8c = 48$

- Divide both sides by 8

Now, divide both sides of the equation by 8 to solve for $c$.$ \frac{8c}{8} = \frac{48}{8}$This simplifies to:$c = 6$

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Key Concepts

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

isolate the variable

When solving linear equations, the first step is to isolate the variable. The goal here is to get the variable on one side of the equation by itself.
This allows you to see what the variable equals. For example, in the equation:\br> \ $8c - 12 = 36$ \ The term containing the variable is $8c$. To isolate $8c$, we need to move any other terms to the opposite side of the equation. In our case, we need to get rid of $-12$.
You can do this by performing operations that will cancel out or 'move' these other terms without changing the balance of the equation. Isolating the variable sets the stage for actually determining its value.

addition property of equality

The addition property of equality is a fundamental tool in solving equations. It states that you can add the same number to both sides of an equation, and the equation will still hold true.
For our equation, $8c - 12 = 36$, we add 12 to both sides to cancel out the $-12$. This gives us: \ $8c - 12 + 12 = 36 + 12$ \ Simplifying this, we get: \ $8c = 48$ \ By adding 12 to both sides, we have successfully removed the $-12$ and simplified the equation further, making the path to solving for $c$ clearer.

division property of equality

After using the addition property of equality, we apply the division property of equality to solve for the variable. This property states that you can divide both sides of an equation by the same nonzero number and the equation will still be balanced.
Looking at our simplified equation: \ $8c = 48$ \ We can divide both sides by 8 to isolate $c$: \ $ \frac{8c}{8} = \frac{48}{8} $ \ Simplifying this, we find: \ $c = 6$ \ By dividing both sides by 8, we isolate $c$ and find its value. This process confirms that solving an equation often involves both addition and division properties of equality to isolate the variable and solve for it.

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91影视

Solve the equation. $$8 c-12=36$$

Short Answer

Step by step solution

- Add 12 to both sides

- Divide both sides by 8

Key Concepts

isolate the variable

addition property of equality

division property of equality

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