Solve The Equation For $y$. $-\frac{(y+8.5)}{4}=4.3$Show Your Work Here:$y=$

by ADMIN 79 views

=====================================================

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, −(y+8.5)4=4.3-\frac{(y+8.5)}{4}=4.3, and provide a step-by-step guide on how to arrive at the solution.

Understanding the Equation

The given equation is a linear equation in one variable, yy. It involves a fraction, which can be simplified to solve for yy. The equation is:

−(y+8.5)4=4.3-\frac{(y+8.5)}{4}=4.3

Step 1: Multiply Both Sides by 4

To eliminate the fraction, we can multiply both sides of the equation by 4. This will help us simplify the equation and make it easier to solve for yy.

−(y+8.5)4×4=4.3×4-\frac{(y+8.5)}{4} \times 4 = 4.3 \times 4

−(y+8.5)=17.2-(y+8.5) = 17.2

Step 2: Distribute the Negative Sign

The negative sign in front of the parentheses can be distributed to each term inside the parentheses.

−(y+8.5)=−y−8.5-(y+8.5) = -y - 8.5

So, the equation becomes:

−y−8.5=17.2-y - 8.5 = 17.2

Step 3: Add 8.5 to Both Sides

To isolate the term involving yy, we can add 8.5 to both sides of the equation.

−y−8.5+8.5=17.2+8.5-y - 8.5 + 8.5 = 17.2 + 8.5

−y=25.7-y = 25.7

Step 4: Multiply Both Sides by -1

To solve for yy, we need to get rid of the negative sign in front of the yy term. We can do this by multiplying both sides of the equation by -1.

−y×−1=25.7×−1-y \times -1 = 25.7 \times -1

y=−25.7y = -25.7

Conclusion

In this article, we have solved the linear equation −(y+8.5)4=4.3-\frac{(y+8.5)}{4}=4.3 using a step-by-step approach. We have multiplied both sides by 4 to eliminate the fraction, distributed the negative sign, added 8.5 to both sides, and finally multiplied both sides by -1 to solve for yy. The solution to the equation is y=−25.7y = -25.7.

Tips and Tricks

  • When solving linear equations, it's essential to follow the order of operations (PEMDAS) to ensure that you are performing the operations in the correct order.
  • When multiplying or dividing both sides of an equation by a negative number, be sure to change the sign of each term.
  • When adding or subtracting both sides of an equation by a number, be sure to change the sign of each term.

Frequently Asked Questions

  • Q: What is the solution to the equation −(y+8.5)4=4.3-\frac{(y+8.5)}{4}=4.3? A: The solution to the equation is y=−25.7y = -25.7.
  • Q: How do I solve a linear equation with a fraction? A: To solve a linear equation with a fraction, you can multiply both sides of the equation by the denominator to eliminate the fraction.
  • Q: What is the order of operations (PEMDAS)? A: The order of operations (PEMDAS) is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

=====================================

Introduction

In our previous article, we provided a step-by-step guide on how to solve the linear equation −(y+8.5)4=4.3-\frac{(y+8.5)}{4}=4.3. However, we understand that sometimes, students may have questions or doubts about solving linear equations. In this article, we will address some of the most frequently asked questions 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=cax + b = c, where aa, bb, and cc are constants, and xx is the variable.

Q: How do I solve a linear equation with a fraction?

A: To solve a linear equation with a fraction, you can multiply both sides of the equation by the denominator to eliminate the fraction. For example, if you have the equation x2=3\frac{x}{2} = 3, you can multiply both sides by 2 to get x=6x = 6.

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

A: The order of operations (PEMDAS) is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. This means that you should perform operations inside parentheses first, followed by exponents, then multiplication and division, and finally addition and subtraction.

Q: How do I solve a linear equation with multiple variables?

A: To solve a linear equation with multiple variables, you can use the method of substitution or elimination. For example, if you have the equation 2x+3y=52x + 3y = 5 and x−2y=−3x - 2y = -3, you can solve for one variable in terms of the other and then substitute that expression into the other equation.

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=3x + 2 = 3 is a linear equation, while the equation x2+4x+4=0x^2 + 4x + 4 = 0 is a quadratic equation.

Q: How do I graph a linear equation?

A: To graph a linear equation, you can use the slope-intercept form of the equation, which is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept. You can plot the y-intercept on the graph and then use the slope to find other points on the line.

Q: What is the significance of linear equations in real-life applications?

A: Linear equations have numerous real-life applications, including physics, engineering, economics, and computer science. For example, linear equations can be used to model the motion of objects, the flow of fluids, and the growth of populations.

Conclusion

In this article, we have addressed some of the most frequently asked questions about solving linear equations. We hope that this Q&A guide has provided you with a better understanding of linear equations and how to solve them.

Tips and Tricks

  • When solving linear equations, it's essential to follow the order of operations (PEMDAS) to ensure that you are performing the operations in the correct order.
  • When multiplying or dividing both sides of an equation by a negative number, be sure to change the sign of each term.
  • When adding or subtracting both sides of an equation by a number, be sure to change the sign of each term.

Frequently Asked Questions

  • Q: What is the solution to the equation −(y+8.5)4=4.3-\frac{(y+8.5)}{4}=4.3? A: The solution to the equation is y=−25.7y = -25.7.
  • Q: How do I solve a linear equation with a fraction? A: To solve a linear equation with a fraction, you can multiply both sides of the equation by the denominator to eliminate the fraction.
  • Q: What is the order of operations (PEMDAS)? A: The order of operations (PEMDAS) is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.