Which Equation Can Be Used To Solve For $x$?A. $9x - 40 = 90$ B. $9x - 36 = 90$ C. $9x + 36 = 90$ D. $9x + 40 = 90$ Solve For $x$. $x = \square$

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 explore the process of solving linear equations, focusing on the equation $9x - 40 = 90$. We will also examine other options and determine which one can be used to solve for $x$.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable (in this case, $x$) is 1. It can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants. Linear equations can be solved using various methods, including addition, subtraction, multiplication, and division.

Solving the Equation $9x - 40 = 90$

To solve the equation $9x - 40 = 90$, we need to isolate the variable $x$. We can do this by adding 40 to both sides of the equation, which will eliminate the negative term.

# Define the equation
equation = "9x - 40 = 90"

# Add 40 to both sides of the equation
new_equation = "9x = 130"

Next, we can divide both sides of the equation by 9 to solve for $x$.

# Divide both sides of the equation by 9
solution = "x = 130 / 9"

Using a calculator or performing the division, we find that $x = 14.44$ (rounded to two decimal places).

Other Options: Can They Be Used to Solve for $x$?

Let's examine the other options and determine if they can be used to solve for $x$.

Option B: $9x - 36 = 90$

To solve this equation, we can add 36 to both sides, which will eliminate the negative term.

# Define the equation
equation = "9x - 36 = 90"

# Add 36 to both sides of the equation
new_equation = "9x = 126"

Next, we can divide both sides of the equation by 9 to solve for $x$.

# Divide both sides of the equation by 9
solution = "x = 126 / 9"

Using a calculator or performing the division, we find that $x = 14$.

Option C: $9x + 36 = 90$

To solve this equation, we can subtract 36 from both sides, which will eliminate the positive term.

# Define the equation
equation = "9x + 36 = 90"

# Subtract 36 from both sides of the equation
new_equation = "9x = 54"

Next, we can divide both sides of the equation by 9 to solve for $x$.

# Divide both sides of the equation by 9
solution = "x = 54 / 9"

Using a calculator or performing the division, we find that $x = 6$.

Option D: $9x + 40 = 90$

To solve this equation, we can subtract 40 from both sides, which will eliminate the positive term.

# Define the equation
equation = "9x + 40 = 90"

# Subtract 40 from both sides of the equation
new_equation = "9x = 50"

Next, we can divide both sides of the equation by 9 to solve for $x$.

# Divide both sides of the equation by 9
solution = "x = 50 / 9"

Using a calculator or performing the division, we find that $x = 5.56$ (rounded to two decimal places).

Conclusion

In this article, we have explored the process of solving linear equations, focusing on the equation $9x - 40 = 90$. We have also examined other options and determined which one can be used to solve for $x$. By following the steps outlined in this article, students can develop a deeper understanding of linear equations and improve their problem-solving skills.

Key Takeaways

• Linear equations are a fundamental concept in mathematics.
• Solving linear equations involves isolating the variable using addition, subtraction, multiplication, and division.
• The equation $9x - 40 = 90$ can be solved by adding 40 to both sides and then dividing both sides by 9.
• Other options, such as $9x - 36 = 90$, $9x + 36 = 90$, and $9x + 40 = 90$, can also be used to solve for $x$.

Final Answer

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Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (in this case, $x$) is 1. It can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable using addition, subtraction, multiplication, and division. You can start by adding or subtracting the same value to both sides of the equation to eliminate the constant term. Then, you can multiply or divide both sides of the equation by the same value to solve for the variable.

Q: What is the order of operations when solving a linear equation?

A: When solving a linear equation, you should follow the order of operations (PEMDAS):

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

Q: How do I handle fractions when solving a linear equation?

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

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

A: Yes, you can use a calculator to solve a linear equation. However, it's always a good idea to check your work by plugging the solution back into the original equation to make sure it's true.

Q: What if I have a linear equation with a variable on both sides?

A: If you have a linear equation with a variable on both sides, you can add or subtract the same value to both sides of the equation to eliminate the variable on one side. Then, you can solve for the variable using the same steps as before.

Q: Can I solve a linear equation with a negative coefficient?

A: Yes, you can solve a linear equation with a negative coefficient. To do this, you can multiply both sides of the equation by -1 to get a positive coefficient. For example, if you have the equation $-2x = 6$, you can multiply both sides by -1 to get $2x = -6$.

Q: What if I have a linear equation with a decimal coefficient?

A: If you have a linear equation with a decimal coefficient, you can multiply both sides of the equation by 10 to get a whole number coefficient. For example, if you have the equation $0.5x = 3$, you can multiply both sides by 10 to get $5x = 30$.

Q: Can I solve a linear equation with a variable in the denominator?

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

Q: What if I have a linear equation with a negative variable?

A: If you have a linear equation with a negative variable, you can multiply both sides of the equation by -1 to get a positive variable. For example, if you have the equation $-2x = 6$, you can multiply both sides by -1 to get $2x = -6$.

Q: Can I solve a linear equation with a variable in the exponent?

A: Yes, you can solve a linear equation with a variable in the exponent. To do this, you can take the logarithm of both sides of the equation to eliminate the exponent. For example, if you have the equation $2^x = 8$, you can take the logarithm of both sides to get $x = \log_2(8)$.

Q: What if I have a linear equation with a variable in the logarithm?

A: If you have a linear equation with a variable in the logarithm, you can use the property of logarithms to rewrite the equation in a simpler form. For example, if you have the equation $\log_2(x) = 3$, you can rewrite the equation as $x = 2^3$.

Conclusion

In this article, we have answered some of the most frequently asked questions about solving linear equations. We have covered topics such as the order of operations, handling fractions, and solving equations with negative coefficients and variables. By following the steps outlined in this article, you can develop a deeper understanding of linear equations and improve your problem-solving skills.