Solve The Equation Below:$\[ 15t = -36 \\]

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will focus on solving a simple linear equation, $15t = -36$, and provide a step-by-step guide on how to approach it.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable(s) is 1. It can be written in the form $ax = b$, where $a$ and $b$ are constants, and $x$ is the variable. Linear equations can be solved using various methods, including algebraic manipulation and graphical methods.

The Equation to be Solved

The equation we will be solving is $15t = -36$. This is a simple linear equation, and we will use algebraic manipulation to solve it.

Step 1: Isolate the Variable

To solve the equation, we need to isolate the variable $t$. We can do this by dividing both sides of the equation by 15.

# Import necessary modules
import sympy as sp

# Define the variable
t = sp.symbols('t')

# Define the equation
equation = 15*t + 36

# Solve the equation
solution = sp.solve(equation, t)

Step 2: Simplify the Equation

After isolating the variable, we need to simplify the equation. In this case, we can simplify the equation by dividing both sides by 15.

# Simplify the equation
simplified_equation = solution[0]

Step 3: Solve for the Variable

Now that we have simplified the equation, we can solve for the variable $t$. We can do this by evaluating the expression.

# Solve for the variable
t_value = simplified_equation

The Final Answer

The final answer is $\boxed{-\frac{12}{5}}$.

Conclusion

Solving linear equations is a crucial skill for students and professionals alike. In this article, we have provided a step-by-step guide on how to solve a simple linear equation, $15t = -36$. We have used algebraic manipulation to isolate the variable, simplify the equation, and solve for the variable. With practice and patience, anyone can master the art of solving linear equations.

Additional Resources

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

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

Frequently Asked Questions

Q: What is a linear equation? A: A linear equation is an equation in which the highest power of the variable(s) is 1.

Q: How do I solve a linear equation? A: To solve a linear equation, you need to isolate the variable, simplify the equation, and solve for the variable.

Q: What is the final answer to the equation $15t = -36$? A: The final answer is $\boxed{-\frac{12}{5}}$.

Related Topics

• Solving Quadratic Equations
• Solving Polynomial Equations
• Graphing Linear Equations

Glossary

• Linear Equation: An equation in which the highest power of the variable(s) is 1.
• Variable: A symbol or expression that represents a value that can change.
• Constant: A value that does not change.
• Algebraic Manipulation: The process of using mathematical operations to simplify or solve an equation.
  Solving Linear Equations: A Q&A Guide =====================================

Introduction

Solving linear equations is a crucial skill for students and professionals alike. In our previous article, we provided a step-by-step guide on how to solve a simple linear equation, $15t = -36$. In this article, we will answer some 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. It can be written in the form $ax = b$, where $a$ and $b$ 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, simplify the equation, and solve for the variable. Here's a step-by-step guide:

1. Isolate the variable by adding or subtracting the same value to both sides of the equation.
2. Simplify the equation by combining like terms.
3. Solve for the variable by dividing both sides of the equation by the coefficient of the variable.

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, $x + 2 = 5$ is a linear equation, while $x^2 + 4x + 4 = 0$ is a quadratic equation.

Q: How do I graph a linear equation?

A: To graph a linear equation, you need to find two points on the line and plot them on a coordinate plane. You can use the slope-intercept form of a linear equation, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Q: What is the slope-intercept form of a linear equation?

A: The slope-intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. The slope represents the rate of change of the line, while the y-intercept represents the point where the line intersects the y-axis.

Q: How do I find the slope of a linear equation?

A: To find the slope of a linear equation, you need to use the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line.

Q: What is the y-intercept of a linear equation?

A: The y-intercept of a linear equation is the point where the line intersects the y-axis. It is represented by the value of $b$ in the slope-intercept form of a linear equation, $y = mx + b$.

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

A: To solve a system of linear equations, you need to find the values of the variables that satisfy both equations. You can use the substitution method or the elimination method to solve the system.

Q: What is the substitution method?

A: The substitution method is a technique used to solve a system of linear equations by substituting the expression for one variable into the other equation.

Q: What is the elimination method?

A: The elimination method is a technique used to solve a system of linear equations by adding or subtracting the equations to eliminate one of the variables.

Conclusion

Solving linear equations is a crucial skill for students and professionals alike. In this article, we have answered some frequently asked questions about solving linear equations. We hope that this article has provided you with a better understanding of linear equations and how to solve them.

Additional Resources

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

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

Frequently Asked Questions

Q: What is a linear equation? A: A linear equation is an equation in which the highest power of the variable(s) is 1.

Q: How do I solve a linear equation? A: To solve a linear equation, you need to isolate the variable, simplify the equation, and solve for the variable.

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.

Related Topics

• Solving Quadratic Equations
• Solving Polynomial Equations
• Graphing Linear Equations

Glossary

• Linear Equation: An equation in which the highest power of the variable(s) is 1.
• Variable: A symbol or expression that represents a value that can change.
• Constant: A value that does not change.
• Algebraic Manipulation: The process of using mathematical operations to simplify or solve an equation.
• Slope-Intercept Form: The form of a linear equation, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.