Problem 15 Solve. $$ x+3=13 $$... [FREE SOLUTION]

91影视

Elementary Algebra

John Redden

$Math Studyset 91影视 Explanations$ Math

2011 Edition

Chapter 2: Problem 15

Solve. $$ x+3=13 $$

Short Answer

Expert verified

The solution is $x = 10$.

Step by step solution

Understand the Equation

The equation is a simple linear equation in one variable: $x + 3 = 13$. Our goal is to solve for $x$, which means we need to find the value of $x$ that makes the equation true.

Isolate the Variable

To isolate $x$, we need to get rid of the constant term (3) on the same side as $x$. We can do this by subtracting 3 from both sides of the equation to maintain equality: $x + 3 - 3 = 13 - 3$.

Simplify Both Sides

Simplify the equation by carrying out the subtraction: $x = 10$. The 3 and -3 on the left side cancel each other out, leaving us with $x$ alone.

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Key Concepts

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

Understanding Simple Linear Equations

A simple linear equation is one of the most basic forms of algebra. It involves an equation where the highest power of the variable is one. This means the variable appears only raised to the power of one, like in the equation $x + 3 = 13$.
Linear equations are like a balance scale; what you do to one side of the equation, you must do to the other to keep things equal. This makes solving them straightforward, as long as you perform operations consistently on both sides.

Example: $x + 3 = 13$
Objective: Find $x$

Understanding this balance and the goal to solve for the variable is the key to mastering linear equations.

Isolating the Variable

The main objective when solving a linear equation is to isolate the variable. This means getting the variable on one side of the equation by itself. When you isolate the variable, you can easily find its value.

In the equation $x + 3 = 13$, you want to isolate $x$. You do this by removing the constant that is added to $x$ by performing the inverse operation.

Subtract 3 from both sides: $x + 3 - 3 = 13 - 3$
This keeps the equation balanced

Now you've successfully isolated $x$. Isolating the variable is crucial for understanding and solving any linear equation.

Equation Simplification

Equation simplification involves reducing both sides of the equation to reveal the solution more clearly. After performing the operation required to isolate the variable, it's time to simplify the equation.

From the previous step: $x + 3 - 3 = 13 - 3$.
The left side simplifies to $x$, as $+3$ and $-3$ cancel each other out.

Result: $x = 10$

You have found the value of $x$ that satisfies the equation. Simplification not only makes the equation easier to read but also affirms the accuracy of your solution.

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91影视

Solve. $$ x+3=13 $$

Short Answer

Step by step solution

Understand the Equation

Isolate the Variable

Simplify Both Sides

Key Concepts

Understanding Simple Linear Equations

Isolating the Variable

Equation Simplification

One App. One Place for Learning.

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