Problem 6 Solve the equations. $$3 x=27$... [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 7: Problem 6

Solve the equations. $$3 x=27$$

Short Answer

Expert verified

The solution is $ x = 9 $.

Step by step solution

Identify the equation

The given equation is: \[ 3x = 27 \]

Isolate the variable

To solve for $ x $, isolate $ x $ by dividing both sides of the equation by 3. This gives: \[ x = \frac{27}{3} \]

Simplify the expression

Simplify the right side of the equation: \[ x = 9 \]

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Key Concepts

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

Isolate the Variable

One of the key strategies in solving linear equations is isolating the variable. This means getting the unknown variable ($x$in our case) by itself on one side of the equation.
To do this, we perform the same operation on both sides of the equation.In our given equation, $3x = 27$,the variable $x$is being multiplied by 3.To isolate $x$, we need to undo this multiplication by dividing both sides by 3.
After dividing, we get:\[ x = \frac{27}{3} \]By isolating the variable, we place ourselves a step closer to finding its value.

Simplify Expressions

Simplifying expressions is another important concept in basic algebra that often comes hand in hand with isolating the variable. Once you perform the necessary operations to isolate the variable, you may end up with an expression that still needs to be simplified.
In our equation, after isolating $x$, we have:\[ x = \frac{27}{3} \]The expression $\frac{27}{3}$can be simplified. This means performing the division to find a simpler form:\[ x = 9 \]Simplifying expressions helps us get clear and straightforward answers, making calculations easier to understand and more accurate.

Basic Algebra

Understanding and applying basic algebra is essential for solving most equations. Basic algebra involves operations and manipulations of variables and constants to find unknown values.
For example, the given equation $3x = 27$is a simple algebraic equation that requires a basic understanding of multiplication and division to solve.
Here are some general steps in solving such equations:

Identify the equation and the variables involved.
Isolate the variable by performing operations like addition, subtraction, multiplication, or division on both sides.
Simplify the resulting expression to find the value of the variable.

Once these steps are mastered, solving more complex equations becomes manageable. Basic algebra forms the foundation for all higher-level math concepts, so it's crucial to have a good grasp of it from the start.

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91影视

Solve the equations. $$3 x=27$$

Short Answer

Step by step solution

Identify the equation

Isolate the variable

Simplify the expression

Key Concepts

Isolate the Variable

Simplify Expressions

Basic Algebra

One App. One Place for Learning.

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