Match Each Equation With Its Solution:1. $-3 = 1 - X + 2$ 2. $n - 6 + 8n = -6$ 3. $ 2 ( 4 + 7 B ) − 3 = 117 2(4 + 7b) - 3 = 117 2 ( 4 + 7 B ) − 3 = 117 [/tex] 4. $4(-7 - 8x) + 7 = -117$ Solutions: A. 8 B. 0 C. 6 D. 3 Match The Equations With
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 four linear equations and matching each equation with its solution. We will break down each equation step by step, using algebraic techniques to isolate the variable and find the solution.
Equation 1: -3 = 1 - x + 2
Step 1: Simplify the equation
The first step is to simplify the equation by combining like terms.
Combine the constants on the right-hand side:
Step 2: Isolate the variable
Next, we need to isolate the variable x. To do this, we can subtract 3 from both sides of the equation:
Step 3: Solve for x
Finally, we can solve for x by multiplying both sides of the equation by -1:
Equation 2: n - 6 + 8n = -6
Step 1: Simplify the equation
The first step is to simplify the equation by combining like terms.
Combine the n terms on the left-hand side:
Step 2: Isolate the variable
Next, we need to isolate the variable n. To do this, we can add 6 to both sides of the equation:
Step 3: Solve for n
Finally, we can solve for n by dividing both sides of the equation by 9:
Equation 3: 2(4 + 7b) - 3 = 117
Step 1: Simplify the equation
The first step is to simplify the equation by distributing the 2 to the terms inside the parentheses.
Distribute the 2:
Combine the constants on the left-hand side:
Step 2: Isolate the variable
Next, we need to isolate the variable b. To do this, we can subtract 5 from both sides of the equation:
Step 3: Solve for b
Finally, we can solve for b by dividing both sides of the equation by 14:
Equation 4: 4(-7 - 8x) + 7 = -117
Step 1: Simplify the equation
The first step is to simplify the equation by distributing the 4 to the terms inside the parentheses.
Distribute the 4:
Combine the constants on the left-hand side:
Step 2: Isolate the variable
Next, we need to isolate the variable x. To do this, we add 21 to both sides of the equation:
Step 3: Solve for x
Finally, we can solve for x by dividing both sides of the equation by -32:
Conclusion
In this article, we have solved four linear equations and matched each equation with its solution. We have used algebraic techniques to isolate the variable and find the solution for each equation. By following these steps, you can solve linear equations and become more confident in your math skills.
Match the Equations with their Solutions
| Equation | Solution |
|---|---|
| -3 = 1 - x + 2 | c. 6 |
| n - 6 + 8n = -6 | b. 0 |
| 2(4 + 7b) - 3 = 117 | a. 8 |
| 4(-7 - 8x) + 7 = -117 | d. 3 |
Note: The correct match is:
| Equation | Solution | |
|---|---|---|
| -3 = 1 - x + 2 | c. 6 | |
| n - 6 + 8n = -6 | b. 0 | |
| 2(4 + 7b) - 3 = 117 | a. 8 | |
| 4(-7 - 8x) + 7 = -117 | d. 3 |
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 = c, where a, b, and c are constants, and x is the variable.
Q: How do I simplify a linear equation?
A: To simplify a linear equation, you can combine like terms by adding or subtracting the coefficients of the same variable. For example, if you have the equation 2x + 3x = 5, you can combine the x terms by adding 2 and 3, resulting in 5x = 5.
Q: How do I isolate the variable in a linear equation?
A: To isolate the variable in a linear equation, you can use inverse operations to get the variable by itself on one side of the equation. For example, if you have the equation x + 2 = 5, you can subtract 2 from both sides to isolate the variable x.
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, while a quadratic equation is an equation in which the highest power of the variable(s) is 2. For example, the equation x + 2 = 5 is a linear equation, while the equation x^2 + 2x + 1 = 0 is a quadratic equation.
Q: How do I solve a linear equation with fractions?
A: To solve a linear equation with fractions, you can multiply both sides of the equation by the least common multiple (LCM) of the denominators to eliminate the fractions. For example, if you have the equation 1/2x + 1/3 = 2/3, you can multiply both sides by 6 to eliminate the fractions.
Q: Can I use a calculator to solve a linear equation?
A: Yes, you can use a calculator to solve a linear equation. However, it's always a good idea to check your work by plugging the solution back into the original equation to make sure it's true.
Q: What are some common mistakes to avoid when solving linear equations?
A: Some common mistakes to avoid when solving linear equations include:
- Not combining like terms
- Not using inverse operations to isolate the variable
- Not checking your work by plugging the solution back into the original equation
- Not using the correct order of operations (PEMDAS)
Q: How can I practice solving linear equations?
A: You can practice solving linear equations by working through practice problems in a textbook or online resource. You can also try solving linear equations on your own by creating your own problems or using a worksheet.
Q: What are some real-world applications of linear equations?
A: Linear equations have many real-world applications, including:
- Modeling population growth
- Calculating interest rates
- Determining the cost of goods
- Solving problems in physics and engineering
By practicing linear equations and understanding their real-world applications, you can become more confident in your math skills and better equipped to tackle complex problems.