Select All The True Equations. (Select All That Apply.)A. 3 X = 90 3x = 90 3 X = 90 B. X + Y = 90 X + Y = 90 X + Y = 90 C. 5 X = 180 5x = 180 5 X = 180 D. X + Y + 2 Z = 180 X + Y + 2z = 180 X + Y + 2 Z = 180 E. X + Y + Z = 360 X + Y + Z = 360 X + Y + Z = 360 3. Discuss Your Selections With A Classmate.

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 the process of selecting true equations from a given set of options. We will examine each equation and determine whether it is true or false, and discuss the reasoning behind our selections.

Understanding 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 + by + cz + ... = d

where a, b, c, ... are constants, and x, y, z, ... are variables.

Analyzing the Options

Let's examine each of the options given:

A. $3x = 90$

To determine whether this equation is true, we need to check if it is possible to find a value of x that satisfies the equation. We can do this by dividing both sides of the equation by 3:

$$\frac{3x}{3} = \frac{90}{3}$$

This simplifies to:

$$x = 30$$

Since we have found a value of x that satisfies the equation, we can conclude that this equation is true.

B. $x + y = 90$

This equation is also true, as we can find values of x and y that satisfy the equation. For example, if x = 30 and y = 60, then the equation is satisfied.

C. $5x = 180$

To determine whether this equation is true, we need to check if it is possible to find a value of x that satisfies the equation. We can do this by dividing both sides of the equation by 5:

$$\frac{5x}{5} = \frac{180}{5}$$

This simplifies to:

$$x = 36$$

Since we have found a value of x that satisfies the equation, we can conclude that this equation is true.

D. $x + y + 2z = 180$

This equation is also true, as we can find values of x, y, and z that satisfy the equation. For example, if x = 30, y = 60, and z = 0, then the equation is satisfied.

E. $x + y + z = 360$

This equation is not true, as it is not possible to find values of x, y, and z that satisfy the equation. For example, if x = 30, y = 60, and z = 0, then the sum of x, y, and z is 90, not 360.

Conclusion

In conclusion, the true equations from the given set of options are:

• A. $3x = 90$
• B. $x + y = 90$
• C. $5x = 180$
• D. $x + y + 2z = 180$

These equations are all true, as we have found values of the variables that satisfy each equation. The equation that is not true is E. $x + y + z = 360$, as it is not possible to find values of x, y, and z that satisfy the equation.

Discussion with a Classmate

When discussing this problem with a classmate, we can ask each other questions such as:

• What is the definition of a linear equation?
• How do we determine whether an equation is true or false?
• What are some examples of true and false linear equations?

By discussing this problem with a classmate, we can gain a deeper understanding of the concept of linear equations and how to solve them.

Common Mistakes to Avoid

When solving linear equations, there are several common mistakes to avoid:

• Not checking if the equation is true or false
• Not finding values of the variables that satisfy the equation
• Not simplifying the equation to its simplest form

By avoiding these common mistakes, we can ensure that we are solving linear equations correctly and accurately.

Real-World Applications

Linear equations have many real-world applications, such as:

• Modeling population growth
• Calculating the cost of goods
• Determining the amount of time it takes to complete a task

By understanding how to solve linear equations, we can apply this knowledge to real-world problems and make informed decisions.

Conclusion

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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 + by + cz + ... = d

where a, b, c, ... are constants, and x, y, z, ... are variables.

Q: How do I determine whether a linear equation is true or false?

A: To determine whether a linear equation is true or false, you need to check if it is possible to find a value of the variable(s) that satisfies the equation. You can do this by:

• Dividing both sides of the equation by a constant
• Adding or subtracting a constant from both sides of the equation
• Multiplying or dividing both sides of the equation by a constant

If you can find a value of the variable(s) that satisfies the equation, then the equation is true. If you cannot find a value of the variable(s) that satisfies the equation, then the equation is false.

Q: What are some examples of true and false linear equations?

A: Here are some examples of true and false linear equations:

• True: 2x = 6 (because x = 3 satisfies the equation)
• False: 2x = 5 (because there is no value of x that satisfies the equation)
• True: x + 2 = 5 (because x = 3 satisfies the equation)
• False: x + 2 = 3 (because there is no value of x that satisfies the equation)

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable(s) on one side of the equation. You can do this by:

• Adding or subtracting a constant from both sides of the equation
• Multiplying or dividing both sides of the equation by a constant
• Using inverse operations to isolate the variable(s)

For example, to solve the equation 2x + 3 = 7, you can subtract 3 from both sides of the equation to get:

2x = 4

Then, you can divide both sides of the equation by 2 to get:

x = 2

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

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

• Not checking if the equation is true or false
• Not finding values of the variables that satisfy the equation
• Not simplifying the equation to its simplest form
• Not using inverse operations to isolate the variable(s)

Q: How do I apply linear equations to real-world problems?

A: Linear equations have many real-world applications, such as:

• Modeling population growth
• Calculating the cost of goods
• Determining the amount of time it takes to complete a task

To apply linear equations to real-world problems, you need to:

• Identify the variables and constants in the problem
• Write an equation that represents the problem
• Solve the equation to find the value of the variable(s)

For example, if you want to calculate the cost of goods, you can write an equation that represents the cost of the goods, such as:

Cost = Price x Quantity

Then, you can solve the equation to find the cost of the goods.

Q: What are some tips for solving linear equations?

A: Here are some tips for solving linear equations:

• Read the equation carefully and understand what it is asking
• Use inverse operations to isolate the variable(s)
• Simplify the equation to its simplest form
• Check your work to make sure the equation is true or false

By following these tips, you can solve linear equations accurately and efficiently.

Conclusion

In conclusion, linear equations are an important concept in mathematics, and solving them is a crucial skill for students to master. By understanding the concept of linear equations and how to solve them, you can apply this knowledge to real-world problems and make informed decisions. Remember to avoid common mistakes, use inverse operations, and simplify the equation to its simplest form. With practice and patience, you can become proficient in solving linear equations.