Solve For $y$. Round Your Answer To The Nearest Tenth And Explain All Steps. − 3 = 45 + 4 Y -3 = 45 + 4y − 3 = 45 + 4 Y

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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 solving a linear equation for the variable y, using a simple yet effective approach. We will take a step-by-step approach to solve the equation, and provide explanations for each step.

The Equation

The given equation is:

−3=45+4y-3 = 45 + 4y

Our goal is to solve for y, rounding our answer to the nearest tenth.

Step 1: Isolate the Variable

To solve for y, we need to isolate the variable on one side of the equation. In this case, we have a constant term on the left-hand side, and a variable term on the right-hand side. To isolate the variable, we need to get rid of the constant term on the right-hand side.

We can do this by subtracting 45 from both sides of the equation:

−3−45=45+4y−45-3 - 45 = 45 + 4y - 45

This simplifies to:

−48=4y-48 = 4y

Step 2: Divide Both Sides by the Coefficient

Now that we have isolated the variable, we need to get rid of the coefficient (4) that is being multiplied by the variable. To do this, we can divide both sides of the equation by 4:

−484=4y4\frac{-48}{4} = \frac{4y}{4}

This simplifies to:

−12=y-12 = y

Step 3: Round the Answer to the Nearest Tenth

Finally, we need to round our answer to the nearest tenth. In this case, our answer is -12, which is already a whole number. However, if we were to round a decimal value to the nearest tenth, we would follow these steps:

  • If the hundredth place is 5 or greater, we round up.
  • If the hundredth place is 4 or less, we round down.

In this case, our answer is -12, which is a whole number, so we don't need to round it.

Conclusion

In this article, we solved a linear equation for the variable y, using a step-by-step approach. We isolated the variable, divided both sides by the coefficient, and rounded our answer to the nearest tenth. By following these steps, we were able to solve the equation and find the value of y.

Tips and Tricks

  • When solving linear equations, it's essential to follow the order of operations (PEMDAS).
  • Make sure to isolate the variable on one side of the equation before dividing both sides by the coefficient.
  • When rounding decimal values to the nearest tenth, remember to follow the rules for rounding up and down.

Common Mistakes

  • Failing to isolate the variable before dividing both sides by the coefficient.
  • Not following the order of operations (PEMDAS).
  • Rounding decimal values incorrectly.

Real-World Applications

Linear equations have numerous real-world applications, including:

  • Physics: Linear equations are used to describe the motion of objects under constant acceleration.
  • Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
  • Economics: Linear equations are used to model economic systems and make predictions about future trends.

Conclusion

Introduction

In our previous article, we explored the step-by-step process of solving linear equations. However, we know that practice makes perfect, and there's no better way to learn than by asking questions and getting answers. In this article, we'll address some common questions and concerns that students may have when solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (usually x or y) is 1. In other words, it's an equation that can be written in the form ax + b = c, where a, b, and c are constants.

Q: How do I know if an equation is linear or not?

A: To determine if an equation is linear, look for the highest power of the variable. If it's 1, then the equation is linear. If it's greater than 1, then the equation is not linear.

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. For example, the equation x + 2 = 3 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, follow these steps:

  1. Multiply both sides of the equation by the least common multiple (LCM) of the denominators.
  2. Simplify the equation by canceling out any common factors.
  3. Solve for the variable as usual.

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

A: The order of operations (PEMDAS) is a set of rules that tells us 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 solve a linear equation with decimals?

A: To solve a linear equation with decimals, follow these steps:

  1. Multiply both sides of the equation by 10 to eliminate the decimal point.
  2. Solve for the variable as usual.
  3. Divide the result by 10 to get the final answer.

Q: What is the difference between a linear equation and a system of linear equations?

A: A linear equation is a single equation with one variable, while a system of linear equations is a set of two or more equations with two or more variables. For example, the equation x + 2 = 3 is a linear equation, while the system of equations x + 2y = 3 and 2x - 3y = 4 is a system of linear equations.

Q: How do I solve a system of linear equations?

A: To solve a system of linear equations, follow these steps:

  1. Use the substitution method or the elimination method to solve for one variable.
  2. Substitute the value of the variable into one of the original equations to solve for the other variable.
  3. Check your answer by plugging it back into both original equations.

Conclusion

In this article, we addressed some common questions and concerns that students may have when solving linear equations. By following the step-by-step process and using the order of operations (PEMDAS), you'll be able to solve linear equations with ease. Remember to practice, practice, practice, and don't be afraid to ask questions if you're unsure. Happy solving!