Problem 1 In questions 1-24 solve each equ... [FREE SOLUTION]

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Chapter 7: Problem 1

In questions 1-24 solve each equation: $$ 7 x=14 $$

Short Answer

Expert verified

The solution is $x = 2$.

Step by step solution

Identify the Equation

The given equation is $7x = 14$. We need to solve for $x$.

Isolate the Variable

To find the value of $x$, we need to get $x$ by itself on one side of the equation. Currently, $x$ is multiplied by 7. To isolate $x$, we will divide both sides of the equation by 7.

Perform Division

Divide both sides of the equation by 7: $\frac{7x}{7} = \frac{14}{7}$.

Simplify the Equation

Simplifying both sides gives $x = 2$. Since we have isolated $x$, this is our solution.

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Key Concepts

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

Solving Equations

When we talk about solving equations, we're referring to the process of finding the value of the variable that makes the equation true. An equation is like a balance scale; what you do on one side, you must also do to the other. These operations ensure that both sides remain in balance.

Here鈥檚 how to approach solving a linear equation:

Identify the equation and the variable you need to solve for.
Perform the same operation on both sides to maintain balance.
Simplify each step to gradually get closer to the solution.

Using these principles, solving simple equations like $7x = 14$ becomes straightforward. By performing operations that simplify and isolate the variable, you find the solution.

Isolation of Variables

The core objective when solving equations is often to isolate the variable. This means getting the variable by itself on one side of the equal sign. In the equation $7x = 14$, our goal is to have 'x' alone on one side.

Here鈥檚 how you achieve that:

Identify the operation currently being performed on the variable (e.g., multiplication, addition).
Do the inverse (opposite) operation on both sides of the equation to move other numbers away from the variable.

For example, in $7x = 14$, since 'x' is multiplied by 7, you should divide both sides by 7. This inverse operation helps you isolate 'x'.

Division in Algebra

Division is a fundamental operation in algebra, especially when it comes to solving equations. It helps us reverse multiplication, enabling us to isolate variables.

To divide in an equation:

Identify the term or number by which the variable is multiplied.
Divide every term in the equation by this number.
Simplify the resulting expressions to get your answer.

Take the equation $7x = 14$ as an example. We divide each side by 7 to get $x = 2$. This division is crucial as it simplifies the equation, allowing us to find the exact value of 'x'. By consistently applying division in algebra, solving linear equations becomes a systematic and logical process.

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91影视

In questions 1-24 solve each equation: $$ 7 x=14 $$

Short Answer

Step by step solution

Identify the Equation

Isolate the Variable

Perform Division

Simplify the Equation

Key Concepts

Solving Equations

Isolation of Variables

Division in Algebra

One App. One Place for Learning.

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