Which Values Are Solutions To 90 \textless − 30 P + 15 90 \ \textless \ -30p + 15 90 \textless − 30 P + 15 ? Check All That Apply.- P = − 10 P = -10 P = − 10 - P = 0 P = 0 P = 0 - P = − 2.5 P = -2.5 P = − 2.5 - P = 3 P = 3 P = 3 - P = − 5 P = -5 P = − 5 - P = 7.6 P = 7.6 P = 7.6

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 a specific linear equation, $90 \ \textless \ -30p + 15$, and determine the values of $p$ that satisfy the equation. We will also explore the different methods of solving linear equations and provide a step-by-step guide on how to solve them.

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 $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable. Linear equations can be solved using various methods, including algebraic manipulation, graphing, and substitution.

The Equation $90 \ \textless \ -30p + 15$

The given equation is $90 \ \textless \ -30p + 15$. To solve for $p$, we need to isolate the variable $p$ on one side of the equation. We can start by subtracting 15 from both sides of the equation:

$$90 - 15 \ \textless \ -30p + 15 - 15$$

This simplifies to:

$$75 \ \textless \ -30p$$

Next, we can divide both sides of the equation by -30:

$$\frac{75}{-30} \ \textless \ \frac{-30p}{-30}$$

This simplifies to:

$$-2.5 \ \textless \ p$$

Solving for $p$

Now that we have the simplified equation, $-2.5 \ \textless \ p$, we can determine the values of $p$ that satisfy the equation. To do this, we need to find the values of $p$ that are greater than -2.5.

Checking the Options

Let's check the options given in the problem:

• $p = -10$: This value is less than -2.5, so it does not satisfy the equation.
• $p = 0$: This value is greater than -2.5, so it satisfies the equation.
• $p = -2.5$: This value is equal to -2.5, so it satisfies the equation.
• $p = 3$: This value is greater than -2.5, so it satisfies the equation.
• $p = -5$: This value is less than -2.5, so it does not satisfy the equation.
• $p = 7.6$: This value is greater than -2.5, so it satisfies the equation.

Conclusion

In conclusion, the values of $p$ that satisfy the equation $90 \ \textless \ -30p + 15$ are $p = 0$, $p = -2.5$, $p = 3$, and $p = 7.6$. These values are greater than -2.5, which is the solution to the equation.

Additional Tips and Tricks

When solving linear equations, it's essential to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

By following these steps and using the correct order of operations, you can solve linear equations with ease.

Common Mistakes to Avoid

When solving linear equations, it's easy to make mistakes. Here are some common mistakes to avoid:

• Not following the order of operations (PEMDAS)
• Not isolating the variable on one side of the equation
• Not checking the solution to ensure it satisfies the original equation

By avoiding these common mistakes, you can ensure that your solutions are accurate and reliable.

Final Thoughts

Introduction

In our previous article, we explored the concept of linear equations and how to solve them. We also provided a step-by-step guide on how to solve the equation $90 \ \textless \ -30p + 15$. In this article, we will answer some frequently asked questions (FAQs) about solving linear equations.

Q&A

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 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 using algebraic manipulation, such as adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when solving an equation. The acronym PEMDAS stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I check my solution to ensure it satisfies the original equation?

A: To check your solution, plug the value of the variable back into the original equation and see if it is true. If the equation 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 following the order of operations (PEMDAS)
• Not isolating the variable on one side of the equation
• Not checking the solution to ensure it satisfies the original equation

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

A: Yes, you can use a calculator to solve linear equations. However, it's essential to understand the concept of solving linear equations and how to apply the order of operations (PEMDAS) to ensure that your solution is accurate.

Q: How do I graph a linear equation?

A: To graph a linear equation, you can use a graphing calculator or a graphing tool on a computer. You can also use a coordinate plane to plot points and draw a line that represents the equation.

Q: Can I solve linear equations with variables on both sides of the equation?

A: Yes, you can solve linear equations with variables on both sides of the equation. To do this, you need to use algebraic manipulation to isolate the variable on one side of the equation.

Q: How do I solve linear equations with fractions?

A: To solve linear equations with fractions, you need to eliminate the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators.

Conclusion

Solving linear equations is a crucial skill for students to master. By following the steps outlined in this article and using the correct order of operations (PEMDAS), you can solve linear equations with ease. Remember to check your solutions to ensure they satisfy the original equation, and avoid common mistakes like not following the order of operations or not isolating the variable on one side of the equation. With practice and patience, you can become a master of solving linear equations.

Additional Resources

For more information on solving linear equations, check out the following resources:

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

Final Thoughts

Solving linear equations is a fundamental concept in mathematics, and it's essential to understand how to solve them. By following the steps outlined in this article and using the correct order of operations (PEMDAS), you can solve linear equations with ease. Remember to check your solutions to ensure they satisfy the original equation, and avoid common mistakes like not following the order of operations or not isolating the variable on one side of the equation. With practice and patience, you can become a master of solving linear equations.