Which Equation Can Be Used To Solve For $x$?A. $10x + 80 = 180$B. $10x + 5 = 75$C. $15x + 75 = 0$

**Which Equation Can Be Used to Solve for $x$?**

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Introduction

In mathematics, solving equations is a fundamental concept that is used to find the value of unknown variables. There are various types of equations, and each type requires a specific method to solve for the unknown variable. In this article, we will discuss three different equations and determine which one can be used to solve for $x$.

Equation A: $10x + 80 = 180$

Equation A is a linear equation that involves a single variable $x$. To solve for $x$, we need to isolate the variable on one side of the equation. We can start by subtracting 80 from both sides of the equation:

$$10x + 80 - 80 = 180 - 80$$

This simplifies to:

$$10x = 100$$

Next, we can divide both sides of the equation by 10 to solve for $x$:

$$\frac{10x}{10} = \frac{100}{10}$$

This gives us:

$$x = 10$$

Equation B: $10x + 5 = 75$

Equation B is also a linear equation that involves a single variable $x$. To solve for $x$, we need to isolate the variable on one side of the equation. We can start by subtracting 5 from both sides of the equation:

$$10x + 5 - 5 = 75 - 5$$

This simplifies to:

$$10x = 70$$

Next, we can divide both sides of the equation by 10 to solve for $x$:

$$\frac{10x}{10} = \frac{70}{10}$$

This gives us:

$$x = 7$$

Equation C: $15x + 75 = 0$

Equation C is a linear equation that involves a single variable $x$. To solve for $x$, we need to isolate the variable on one side of the equation. We can start by subtracting 75 from both sides of the equation:

$$15x + 75 - 75 = 0 - 75$$

This simplifies to:

$$15x = -75$$

Next, we can divide both sides of the equation by 15 to solve for $x$:

$$\frac{15x}{15} = \frac{-75}{15}$$

This gives us:

$$x = -5$$

Conclusion

In conclusion, all three equations can be used to solve for $x$. However, the method used to solve each equation is different. Equation A requires subtracting 80 from both sides of the equation and then dividing both sides by 10. Equation B requires subtracting 5 from both sides of the equation and then dividing both sides by 10. Equation C requires subtracting 75 from both sides of the equation and then dividing both sides by 15.

Frequently Asked Questions

Q: What is the value of $x$ in Equation A?

A: The value of $x$ in Equation A is 10.

Q: What is the value of $x$ in Equation B?

A: The value of $x$ in Equation B is 7.

Q: What is the value of $x$ in Equation C?

A: The value of $x$ in Equation C is -5.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable on one side of the equation. You can do this by adding or subtracting the same value from both sides of the equation, and then 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 that involves a single variable and has a degree of 1. A quadratic equation is an equation that involves a single variable and has a degree of 2.

Q: How do I determine the value of $x$ in a quadratic equation?

A: To determine the value of $x$ in a quadratic equation, you need to use the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Q: What is the quadratic formula?

A: The quadratic formula is a formula that is used to solve quadratic equations. It is given by: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Q: How do I use the quadratic formula to solve a quadratic equation?

A: To use the quadratic formula to solve a quadratic equation, you need to plug in the values of $a$, $b$, and $c$ into the formula and then simplify the expression.

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

A: A linear equation is an equation that involves a single variable and has a degree of 1. A system of linear equations is a set of two or more linear equations that involve the same variables.

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 the method of elimination. The method of substitution involves substituting the value of one variable into the other equation, and then solving for the other variable. The method of elimination involves adding or subtracting the two equations to eliminate one of the variables.

Q: What is the method of substitution?

A: The method of substitution is a method that is used to solve a system of linear equations. It involves substituting the value of one variable into the other equation, and then solving for the other variable.

Q: What is the method of elimination?

A: The method of elimination is a method that is used to solve a system of linear equations. It involves adding or subtracting the two equations to eliminate one of the variables.

Q: How do I determine the value of $x$ in a system of linear equations?

A: To determine the value of $x$ in a system of linear equations, you need to use the method of substitution or the method of elimination.