What Is The Value Of $x$ In The Equation $\frac{5(2x-4)}{3} + 9 = 14$?1) 1.9 2) 3.5 3) 5.3 4) 8.9
In mathematics, solving for x in a linear equation is a fundamental concept that involves isolating the variable x on one side of the equation. In this article, we will explore how to solve for x in a linear equation, using the equation $\frac{5(2x-4)}{3} + 9 = 14$ as an example.
Understanding the Equation
The given equation is a linear equation, which means it can be written in the form of ax + b = c, where a, b, and c are constants. In this case, the equation is $\frac{5(2x-4)}{3} + 9 = 14$. To solve for x, we need to isolate x on one side of the equation.
Step 1: Simplify the Equation
The first step in solving for x is to simplify the equation by getting rid of any fractions. We can do this by multiplying both sides of the equation by the denominator, which is 3.
Step 2: Distribute the 5
Next, we need to distribute the 5 to the terms inside the parentheses.
Step 3: Combine Like Terms
Now, we can combine the like terms on the left-hand side of the equation.
Step 4: Subtract 7 from Both Sides
To isolate x, we need to get rid of the constant term on the left-hand side. We can do this by subtracting 7 from both sides of the equation.
Step 5: Divide Both Sides by 10
Finally, we can solve for x by dividing both sides of the equation by 10.
Simplifying the Fraction
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 5.
Conclusion
In this article, we have learned how to solve for x in a linear equation using the equation $\frac{5(2x-4)}{3} + 9 = 14$ as an example. We simplified the equation, distributed the 5, combined like terms, subtracted 7 from both sides, and finally divided both sides by 10 to solve for x. The value of x is $\frac{7}{2}$, which is equal to 3.5.
Answer
The correct answer is:
- 3.5
Solving for x in a Linear Equation: Q&A =====================================
In our previous article, we explored how to solve for x in a linear equation using the equation $\frac{5(2x-4)}{3} + 9 = 14$ as an example. In this article, we will answer some frequently asked questions about solving for x in a linear equation.
Q: What is a linear equation?
A linear equation is an equation in which the highest power of the variable (x) is 1. It can be written in the form of ax + b = c, where a, b, and c are constants.
Q: How do I know if an equation is linear?
To determine if an equation is linear, look for the highest power of the variable (x). If the highest power is 1, then the equation is linear.
Q: What is the first step in solving for x in a linear equation?
The first step in solving for x in a linear equation is to simplify the equation by getting rid of any fractions. This can be done by multiplying both sides of the equation by the denominator.
Q: How do I distribute a number to the terms inside the parentheses?
To distribute a number to the terms inside the parentheses, multiply the number by each term inside the parentheses.
Q: What is the difference between combining like terms and distributing a number?
Combining like terms involves adding or subtracting terms that have the same variable and exponent. Distributing a number involves multiplying the number by each term inside the parentheses.
Q: How do I subtract a constant from both sides of an equation?
To subtract a constant from both sides of an equation, simply subtract the constant from both sides of the equation.
Q: How do I divide both sides of an equation by a number?
To divide both sides of an equation by a number, simply divide both sides of the equation by the number.
Q: What is the final step in solving for x in a linear equation?
The final step in solving for x in a linear equation is to simplify the fraction, if necessary.
Q: How do I simplify a fraction?
To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor.
Q: What are some common mistakes to avoid when solving for x in a linear equation?
Some common mistakes to avoid when solving for x in a linear equation include:
- Not simplifying the equation before solving for x
- Not distributing the number to the terms inside the parentheses
- Not combining like terms
- Not subtracting the constant from both sides of the equation
- Not dividing both sides of the equation by the number
Conclusion
In this article, we have answered some frequently asked questions about solving for x in a linear equation. We have covered topics such as what a linear equation is, how to simplify the equation, how to distribute a number, how to combine like terms, and how to divide both sides of the equation by a number. By following these steps and avoiding common mistakes, you can solve for x in a linear equation with confidence.
Additional Resources
For more information on solving for x in a linear equation, check out the following resources:
- Khan Academy: Solving Linear Equations
- Mathway: Solving Linear Equations
- Wolfram Alpha: Solving Linear Equations
Practice Problems
Try solving the following linear equations: