Solution to the First Equation

Oct 13, 2025 by talynt.org 86 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 explore two linear equations, $(x-3)=11$ and $-(x-3)=11$ , and provide step-by-step solutions to each equation.

What are Linear Equations?

A linear equation is an equation in which the highest power of the variable (in this case, $x$ ) is 1. Linear equations can be written in the form $ax + b = c$ , where $a$ , $b$ , and $c$ are constants.

Solving the First Equation: $(x-3)=11$

To solve the equation $(x-3)=11$ , we need to isolate the variable $x$ .

Step 1: Add 3 to Both Sides

The first step is to add 3 to both sides of the equation to get rid of the negative term.

(x - 3) = 11
x - 3 + 3 = 11 + 3
x = 14

Step 2: Simplify the Equation

By adding 3 to both sides, we have simplified the equation and isolated the variable $x$ .

Solution to the First Equation

The solution to the equation $(x-3)=11$ is $x = 14$ .

Solving the Second Equation: $-(x-3)=11$

To solve the equation $-(x-3)=11$ , we need to isolate the variable $x$ .

Step 1: Distribute the Negative Sign

The first step is to distribute the negative sign to the term inside the parentheses.

-(x - 3) = 11
-x + 3 = 11

Step 2: Subtract 3 from Both Sides

The next step is to subtract 3 from both sides of the equation to get rid of the positive term.

-x + 3 - 3 = 11 - 3
-x = 8

Step 3: Multiply Both Sides by -1

To isolate the variable $x$ , we need to multiply both sides of the equation by -1.

-x = 8
-x \* -1 = 8 \* -1
x = -8

Step 4: Simplify the Equation

By multiplying both sides by -1, we have simplified the equation and isolated the variable $x$ .

Solution to the Second Equation

The solution to the equation $-(x-3)=11$ is $x = -8$ .

Conclusion

In this article, we have solved two linear equations, $(x-3)=11$ and $-(x-3)=11$ , and provided step-by-step solutions to each equation. The solutions to the equations are $x = 14$ and $x = -8$ , respectively.

Frequently Asked Questions

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (in this case, $x$ ) is 1.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

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

A: A linear equation has a highest power of 1, while a quadratic equation has a highest power of 2.

Q: Can I use a calculator to solve a linear equation?

A: Yes, you can use a calculator to solve a linear equation, but it's always a good idea to show your work and check your answer.

Q: How do I check my answer?

A: To check your answer, plug the solution back into the original equation and make sure it's true.

Additional Resources

Khan Academy: Linear Equations
Mathway: Linear Equations
Wolfram Alpha: Linear Equations