Solve For $m$.$5m = -35$A. -175 B. -40 C. -30 D. -7

Feb 26, 2025 by ADMIN 57 views

**Solving Linear Equations: A Step-by-Step Guide**

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving linear equations of the form $ax = b$ , where $a$ and $b$ are constants, and $x$ is the variable. We will use the given equation $5m = -35$ as an example to demonstrate the step-by-step process of solving linear equations.

What are Linear Equations?

A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form $ax = b$ , where $a$ and $b$ are constants, and $x$ is the variable. Linear equations can be solved using various methods, including algebraic manipulation, graphing, and substitution.

The Given Equation

The given equation is $5m = -35$ . This is a linear equation in which the highest power of the variable $m$ is 1. Our goal is to solve for $m$ .

Step 1: Isolate the Variable

To solve for $m$ , we need to isolate the variable on one side of the equation. In this case, we can start by dividing both sides of the equation by 5.

# Given equation: 5m = -35
# Divide both sides by 5
m = -35 / 5

Step 2: Simplify the Equation

After dividing both sides of the equation by 5, we get $m = -7$ . This is the solution to the equation.

Answer

The solution to the equation $5m = -35$ is $m = -7$ .

Conclusion

Solving linear equations is an essential skill for students to master. By following the step-by-step process outlined in this article, students can solve linear equations with ease. Remember to isolate the variable on one side of the equation and simplify the equation to find the solution.

Example Solutions

Here are some example solutions to linear equations:

$2x = 6$ : $x = 3$
$4y = -12$ : $y = -3$
$x + 2 = 7$ : $x = 5$

Tips and Tricks

Here are some tips and tricks to help you solve linear equations:

Always isolate the variable on one side of the equation.
Simplify the equation by combining like terms.
Check your solution by plugging it back into the original equation.

Common Mistakes

Here are some common mistakes to avoid when solving linear equations:

Not isolating the variable on one side of the equation.
Not simplifying the equation.
Not checking the solution.

Real-World Applications

Linear equations have many real-world applications, including:

Physics: Linear equations are used to describe the motion of objects.
Engineering: Linear equations are used to design and optimize systems.
Economics: Linear equations are used to model economic systems.

Conclusion

Final Answer

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will provide a Q&A guide to help students understand and solve linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form $ax = b$ , where $a$ and $b$ are constants, and $x$ is the variable.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable on one side of the equation. You can do this by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: What is the first step in solving a linear equation?

A: The first step in solving a linear equation is to isolate the variable on one side of the equation. You can do this by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: How do I simplify a linear equation?

A: To simplify a linear equation, you need to combine like terms. Like terms are terms that have the same variable and exponent. For example, $2x + 3x$ can be simplified to $5x$ .

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. A quadratic equation is an equation in which the highest power of the variable(s) is 2.

Q: How do I check my solution to a linear equation?

A: To check your solution to a linear equation, you need to plug it back into the original equation and see if it is true. If it is true, then your solution is correct.

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

Not isolating the variable on one side of the equation.
Not simplifying the equation.
Not checking the solution.

Q: How do I use linear equations in real-world applications?

A: Linear equations have many real-world applications, including:

Physics: Linear equations are used to describe the motion of objects.
Engineering: Linear equations are used to design and optimize systems.
Economics: Linear equations are used to model economic systems.

Q: What are some examples of linear equations?

A: Some examples of linear equations include:

$2x = 6$
$4y = -12$
$x + 2 = 7$

Q: How do I solve a linear equation with fractions?

A: To solve a linear equation with fractions, you need to get rid of the fractions by multiplying both sides of the equation by the denominator.

Q: What is the difference between a linear equation and a system of linear equations?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. A system of linear equations is a set of two or more linear equations that are solved together.

Q: How do I solve a system of linear equations?

A: To solve a system of linear equations, you need to solve one of the equations for one of the variables and then substitute that expression into the other equation.

Conclusion

Final Answer

The final answer is: $\boxed{-7}$