Match Each Equation With Its Solution.Equation: 1. { X - 6 = -4 $}$ 2. { X + 3 = -7 $}$ 3. { 0.5x = 5 $}$Solution: A. { X = -0.4 $}$ B. { X = 10 $}$ C. { X = 2 $}$ D. [$ X =

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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 matching each equation with its solution. We will cover three different equations and provide step-by-step solutions to help you understand the process.

Equation 1: x - 6 = -4

Step 1: Add 6 to both sides of the equation

To isolate the variable x, we need to get rid of the constant term -6. We can do this by adding 6 to both sides of the equation.

x - 6 + 6 = -4 + 6

Step 2: Simplify the equation

After adding 6 to both sides, the equation becomes:

x = 2

Conclusion

The solution to the equation x - 6 = -4 is x = 2.

Equation 2: x + 3 = -7

Step 1: Subtract 3 from both sides of the equation

To isolate the variable x, we need to get rid of the constant term 3. We can do this by subtracting 3 from both sides of the equation.

x + 3 - 3 = -7 - 3

Step 2: Simplify the equation

After subtracting 3 from both sides, the equation becomes:

x = -10

Conclusion

The solution to the equation x + 3 = -7 is x = -10.

Equation 3: 0.5x = 5

Step 1: Multiply both sides of the equation by 2

To isolate the variable x, we need to get rid of the coefficient 0.5. We can do this by multiplying both sides of the equation by 2.

0.5x \* 2 = 5 \* 2

Step 2: Simplify the equation

After multiplying both sides by 2, the equation becomes:

x = 10

Conclusion

The solution to the equation 0.5x = 5 is x = 10.

Matching the Equations with their Solutions

Now that we have solved each equation, let's match them with their solutions.

Equation Solution
x - 6 = -4 x = 2
x + 3 = -7 x = -10
0.5x = 5 x = 10

Discussion

Solving linear equations is an essential skill in mathematics, and it requires a step-by-step approach. By following the steps outlined in this article, you can solve linear equations with ease. Remember to isolate the variable by getting rid of the constant term or coefficient, and then simplify the equation to find the solution.

Conclusion

In conclusion, solving linear equations is a crucial skill in mathematics, and it requires a step-by-step approach. By following the steps outlined in this article, you can solve linear equations with ease. Remember to isolate the variable by getting rid of the constant term or coefficient, and then simplify the equation to find the solution.

Frequently Asked Questions

  • Q: What is a linear equation? A: A linear equation is an equation in which the highest power of the variable is 1.
  • Q: How do I solve a linear equation? A: To solve a linear equation, you need to isolate the variable by getting rid of the constant term or coefficient, and then simplify the equation to find the solution.
  • 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 is 1, while a quadratic equation is an equation in which the highest power of the variable is 2.

References

Glossary

  • Linear Equation: An equation in which the highest power of the variable is 1.
  • Variable: A letter or symbol that represents a value that can change.
  • Constant Term: A number that is added to or subtracted from the variable.
  • Coefficient: A number that is multiplied by the variable.
    Linear Equations Q&A =========================

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 answer some frequently asked questions about linear equations, providing step-by-step explanations and examples to help you understand the concepts.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable is 1. It can be written in the form ax + b = c, where a, b, and c are constants, and x is the variable.

Example:

2x + 3 = 5

In this equation, the highest power of the variable x is 1, so it is a linear equation.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable by getting rid of the constant term or coefficient, and then simplify the equation to find the solution.

Step 1: Add or subtract the same value to both sides of the equation

To isolate the variable, you need to get rid of the constant term or coefficient. You can do this by adding or subtracting the same value to both sides of the equation.

Example:

2x + 3 = 5

Subtract 3 from both sides:

2x = 5 - 3 2x = 2

Step 2: Divide both sides of the equation by the coefficient

To find the value of the variable, you need to divide both sides of the equation by the coefficient.

Example:

2x = 2

Divide both sides by 2:

x = 2/2 x = 1

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 is 1, while a quadratic equation is an equation in which the highest power of the variable is 2.

Example:

Linear equation: 2x + 3 = 5

Quadratic equation: x^2 + 2x + 1 = 0

In the linear equation, the highest power of the variable x is 1, while in the quadratic equation, the highest power of the variable x is 2.

Q: How do I graph a linear equation?

A: To graph a linear equation, you need to find two points on the line and then draw a line through them.

Step 1: Find two points on the line

To find two points on the line, you can substitute different values of the variable into the equation and solve for the corresponding values of the constant term.

Example:

2x + 3 = 5

Substitute x = 0:

2(0) + 3 = 5 3 = 5

Substitute x = 1:

2(1) + 3 = 5 5 = 5

The two points on the line are (0, 3) and (1, 5).

Step 2: Draw a line through the two points

To graph the line, you can draw a line through the two points.

Q: What is the slope of a linear equation?

A: The slope of a linear equation is the ratio of the change in the constant term to the change in the variable.

Example:

2x + 3 = 5

The slope of the line is 2/1 = 2.

Q: How do I find the slope of a linear equation?

A: To find the slope of a linear equation, you can use the formula:

slope = (change in constant term) / (change in variable)

Example:

2x + 3 = 5

The change in the constant term is 5 - 3 = 2, and the change in the variable is 1 - 0 = 1.

The slope of the line is 2/1 = 2.

Conclusion

In conclusion, solving linear equations is a crucial skill in mathematics, and it requires a step-by-step approach. By following the steps outlined in this article, you can solve linear equations with ease. Remember to isolate the variable by getting rid of the constant term or coefficient, and then simplify the equation to find the solution.

Frequently Asked Questions

  • Q: What is a linear equation? A: A linear equation is an equation in which the highest power of the variable is 1.
  • Q: How do I solve a linear equation? A: To solve a linear equation, you need to isolate the variable by getting rid of the constant term or coefficient, and then simplify the equation to find the solution.
  • 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 is 1, while a quadratic equation is an equation in which the highest power of the variable is 2.

References

Glossary

  • Linear Equation: An equation in which the highest power of the variable is 1.
  • Variable: A letter or symbol that represents a value that can change.
  • Constant Term: A number that is added to or subtracted from the variable.
  • Coefficient: A number that is multiplied by the variable.
  • Slope: The ratio of the change in the constant term to the change in the variable.