Solve For { X $} . . . { 2x - 3 = 11 \}

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Introduction

Solving for $x$ in a linear equation is a fundamental concept in mathematics, and it's essential to understand how to isolate the variable in a given equation. In this article, we will focus on solving for $x$ in the equation $2x - 3 = 11$. We will break down the steps involved in solving this equation and provide a clear explanation of each step.

Understanding the Equation

The given equation is $2x - 3 = 11$. This is a linear equation, which means it can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants. In this case, $a = 2$, $b = -3$, and $c = 11$.

Step 1: Add 3 to Both Sides

To solve for $x$, we need to isolate the variable on one side of the equation. The first step is to add 3 to both sides of the equation. This will eliminate the constant term on the left side of the equation.

$$2x - 3 + 3 = 11 + 3$$

$$2x = 14$$

Step 2: Divide Both Sides by 2

Now that we have $2x = 14$, we need to isolate $x$ by dividing both sides of the equation by 2. This will give us the value of $x$.

$$\frac{2x}{2} = \frac{14}{2}$$

$$x = 7$$

Conclusion

In this article, we solved for $x$ in the equation $2x - 3 = 11$. We broke down the steps involved in solving this equation and provided a clear explanation of each step. By following these steps, we were able to isolate the variable $x$ and find its value.

Tips and Tricks

• When solving for $x$, it's essential to follow the order of operations (PEMDAS) to ensure that you are performing the correct operations in the correct order.
• When adding or subtracting a constant to both sides of the equation, make sure to add or subtract the same value to both sides.
• When dividing both sides of the equation by a constant, make sure to divide both sides by the same value.

Real-World Applications

Solving for $x$ in a linear equation has many real-world applications. For example, in physics, you may need to solve for the velocity of an object given its acceleration and time. In finance, you may need to solve for the interest rate on a loan given the principal amount, interest rate, and time. In engineering, you may need to solve for the stress on a material given its Young's modulus and strain.

Common Mistakes

• One common mistake when solving for $x$ is to forget to add or subtract the same value to both sides of the equation.
• Another common mistake is to divide both sides of the equation by a value that is not a constant.
• A third common mistake is to forget to follow the order of operations (PEMDAS).

Final Thoughts

Solving for $x$ in a linear equation is a fundamental concept in mathematics, and it's essential to understand how to isolate the variable in a given equation. By following the steps outlined in this article, you should be able to solve for $x$ in any linear equation. Remember to follow the order of operations (PEMDAS) and to add or subtract the same value to both sides of the equation. With practice and patience, you will become proficient in solving for $x$ and be able to apply this skill to real-world problems.

Additional Resources

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

Conclusion

In conclusion, solving for $x$ in a linear equation is a fundamental concept in mathematics that has many real-world applications. By following the steps outlined in this article, you should be able to solve for $x$ in any linear equation. Remember to follow the order of operations (PEMDAS) and to add or subtract the same value to both sides of the equation. With practice and patience, you will become proficient in solving for $x$ and be able to apply this skill to real-world problems.

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Introduction

In our previous article, we solved for $x$ in the equation $2x - 3 = 11$. We broke down the steps involved in solving this equation and provided a clear explanation of each step. In this article, we will answer some common questions that students often have when solving for $x$ in a linear equation.

Q: What is the first step in solving for $x$ in a linear equation?

A: The first step in solving for $x$ in a linear equation is to add or subtract a constant to both sides of the equation in order to isolate the variable on one side of the equation.

Q: How do I know which operation to perform first?

A: To determine which operation to perform first, you need to look at the equation and identify the variable and the constant. If the variable is on the left side of the equation and the constant is on the right side, you need to add or subtract the constant to both sides of the equation. If the variable is on the right side of the equation and the constant is on the left side, you need to subtract the constant from both sides of the equation.

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:

• P: Parentheses (evaluate expressions inside parentheses first)
• E: Exponents (evaluate any exponential expressions next)
• M: Multiplication and Division (perform multiplication and division operations from left to right)
• A: Addition and Subtraction (perform addition and subtraction operations from left to right)

Q: How do I know when to add or subtract a constant to both sides of the equation?

A: To determine whether to add or subtract a constant to both sides of the equation, you need to look at the equation and identify the variable and the constant. If the variable is on the left side of the equation and the constant is on the right side, you need to add the constant to both sides of the equation. If the variable is on the right side of the equation and the constant is on the left side, you need to subtract the constant from both sides of the 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 is 1. For example, the equation $2x - 3 = 11$ is a linear equation. A quadratic equation is an equation in which the highest power of the variable is 2. For example, the equation $x^2 + 4x + 4 = 0$ is a quadratic equation.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you need to use the quadratic formula, which is:

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

where $a$, $b$, and $c$ are the coefficients of the quadratic equation.

Q: What is the quadratic formula?

A: The quadratic formula is a formula that is used to solve quadratic equations. It is:

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

where $a$, $b$, and $c$ are the coefficients of the quadratic equation.

Q: How do I use the quadratic formula?

A: To use the quadratic formula, you need to plug in the values of $a$, $b$, and $c$ into the formula and simplify. The formula will give you two solutions for $x$.

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

A: A linear equation is an equation in which the highest power of the variable is 1. A system of linear equations is a set of two or more linear equations that are solved simultaneously. For example, the system of linear equations:

$$\begin{align*} 2x - 3 &= 11 \\ x + 2 &= 7 \end{align*}$$

is a system of linear equations.

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

A: To solve a system of linear equations, you need to use the method of substitution or elimination. The method of substitution involves solving one equation for one variable and then substituting that expression into the other equation. The method of elimination involves adding or subtracting the equations to eliminate one variable.

Q: What is the method of substitution?

A: The method of substitution is a method of solving a system of linear equations in which one equation is solved for one variable and then that expression is substituted into the other equation.

Q: What is the method of elimination?

A: The method of elimination is a method of solving a system of linear equations in which the equations are added or subtracted to eliminate one variable.

Q: How do I use the method of substitution?

A: To use the method of substitution, you need to solve one equation for one variable and then substitute that expression into the other equation. The resulting equation will have only one variable, which can be solved for.

Q: How do I use the method of elimination?

A: To use the method of elimination, you need to add or subtract the equations to eliminate one variable. The resulting equation will have only one variable, which can be solved for.

Conclusion

In this article, we answered some common questions that students often have when solving for $x$ in a linear equation. We discussed the order of operations (PEMDAS), the method of substitution, and the method of elimination. We also discussed the difference between a linear equation and a quadratic equation, and how to solve a quadratic equation using the quadratic formula. We hope that this article has been helpful in answering your questions and providing you with a better understanding of how to solve for $x$ in a linear equation.