Solve 3 4 P + 1 3 ( 21 − P ) = 12 \frac{3}{4} P + \frac{1}{3}(21-p) = 12 4 3 ​ P + 3 1 ​ ( 21 − P ) = 12 .

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Introduction

Mathematics is a subject that deals with numbers, quantities, and shapes. It is a fundamental subject that is used in various fields such as science, engineering, economics, and finance. In mathematics, equations are used to represent relationships between variables. Solving equations is an essential skill in mathematics, and it is used to find the value of unknown variables. In this article, we will solve the equation $\frac{3}{4} p + \frac{1}{3}(21-p) = 12$.

Understanding the Equation

The given equation is a linear equation, which means it is an equation in which the highest power of the variable is 1. The equation is $\frac{3}{4} p + \frac{1}{3}(21-p) = 12$. To solve this equation, we need to isolate the variable $p$. The equation has two terms, $\frac{3}{4} p$ and $\frac{1}{3}(21-p)$. We can simplify the equation by combining the like terms.

Simplifying the Equation

To simplify the equation, we need to combine the like terms. The like terms are the terms that have the same variable. In this equation, the like terms are $\frac{3}{4} p$ and $-\frac{1}{3}p$. We can combine these terms by adding them together. The equation becomes $\frac{3}{4} p - \frac{1}{3}p + \frac{1}{3}(21) = 12$.

Combining Like Terms

Now, we can combine the like terms. The like terms are $\frac{3}{4} p$ and $-\frac{1}{3}p$. We can combine these terms by adding them together. The equation becomes $\frac{9}{12} p - \frac{4}{12}p + \frac{1}{3}(21) = 12$. We can simplify the equation by combining the fractions. The equation becomes $\frac{5}{12} p + \frac{1}{3}(21) = 12$.

Simplifying the Equation Further

Now, we can simplify the equation further. We can simplify the term $\frac{1}{3}(21)$ by multiplying the fraction by the number. The equation becomes $\frac{5}{12} p + 7 = 12$.

Isolating the Variable

Now, we can isolate the variable $p$. We can do this by subtracting 7 from both sides of the equation. The equation becomes $\frac{5}{12} p = 5$.

Solving for $p$

Now, we can solve for $p$. We can do this by multiplying both sides of the equation by the reciprocal of $\frac{5}{12}$. The equation becomes $p = \frac{12}{5} \times 5$.

Final Answer

The final answer is $p = 12$.

Conclusion

In this article, we solved the equation $\frac{3}{4} p + \frac{1}{3}(21-p) = 12$. We simplified the equation by combining the like terms and isolating the variable $p$. We then solved for $p$ by multiplying both sides of the equation by the reciprocal of $\frac{5}{12}$. The final answer is $p = 12$.

Step-by-Step Solution

Here is the step-by-step solution to the equation:

1. Simplify the equation by combining the like terms: $\frac{3}{4} p + \frac{1}{3}(21-p) = 12$
2. Combine the like terms: $\frac{9}{12} p - \frac{4}{12}p + \frac{1}{3}(21) = 12$
3. Simplify the equation further: $\frac{5}{12} p + \frac{1}{3}(21) = 12$
4. Simplify the term $\frac{1}{3}(21)$: $\frac{5}{12} p + 7 = 12$
5. Isolate the variable $p$: $\frac{5}{12} p = 5$
6. Solve for $p$: $p = \frac{12}{5} \times 5$

Frequently Asked Questions

Here are some frequently asked questions about solving the equation $\frac{3}{4} p + \frac{1}{3}(21-p) = 12$:

• Q: What is the final answer to the equation? A: The final answer is $p = 12$.
• Q: How do I simplify the equation? A: You can simplify the equation by combining the like terms and isolating the variable $p$.
• Q: How do I solve for $p$? A: You can solve for $p$ by multiplying both sides of the equation by the reciprocal of $\frac{5}{12}$.

References

Here are some references that you can use to learn more about solving equations:

• [1] Khan Academy. (n.d.). Solving Linear Equations. Retrieved from https://www.khanacademy.org/math/algebra/x2f1d7c4f0d0d/solving-linear-equations
• [2] Mathway. (n.d.). Solving Linear Equations. Retrieved from https://www.mathway.com/subjects/linear-equations
• [3] Wolfram Alpha. (n.d.). Solving Linear Equations. Retrieved from https://www.wolframalpha.com/input/?i=solving+linear+equations
  

Introduction

Solving equations is an essential skill in mathematics, and it is used to find the value of unknown variables. In this article, we will answer some frequently asked questions about solving equations.

Q: What is an equation?

A: An equation is a statement that says two things are equal. It is a mathematical statement that contains an equal sign (=) and two expressions on either side of the equal sign.

Q: What is a linear equation?

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

Q: How do I simplify an equation?

A: You can simplify an equation by combining like terms and isolating the variable. Like terms are terms that have the same variable, and isolating the variable means getting the variable by itself on one side of the equation.

Q: How do I solve for a variable?

A: You can solve for a variable by isolating the variable on one side of the equation. This means getting the variable by itself on one side of the equation, and everything else on the other side.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when you have multiple operations in an expression. The order of operations is:

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

Q: How do I solve a quadratic equation?

A: A quadratic equation is an equation in which the highest power of the variable is 2. To solve a quadratic equation, you can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where a, b, and c are constants.

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, while a quadratic equation is an equation in which the highest power of the variable is 2.

Q: How do I graph an equation?

A: To graph an equation, you can use a graphing calculator or a graphing software. You can also use a coordinate plane to plot points and draw a line.

Q: What is the equation of a line?

A: The equation of a line is a linear equation that can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.

Q: How do I find the slope of a line?

A: To find the slope of a line, you can use the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

Q: What is the y-intercept of a line?

A: The y-intercept of a line is the point where the line intersects the y-axis. It is the value of y when x is equal to 0.

Q: How do I find the y-intercept of a line?

A: To find the y-intercept of a line, you can use the equation y = mx + b, where m is the slope of the line and b is the y-intercept.

Q: What is the equation of a circle?

A: The equation of a circle is a quadratic equation that can be written in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.

Q: How do I find the center and radius of a circle?

A: To find the center and radius of a circle, you can use the equation (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.

Q: What is the equation of an ellipse?

A: The equation of an ellipse is a quadratic equation that can be written in the form ((x - h)^2 / a^2) + ((y - k)^2 / b^2) = 1, where (h, k) is the center of the ellipse and a and b are the semi-major and semi-minor axes.

Q: How do I find the center and axes of an ellipse?

A: To find the center and axes of an ellipse, you can use the equation ((x - h)^2 / a^2) + ((y - k)^2 / b^2) = 1, where (h, k) is the center of the ellipse and a and b are the semi-major and semi-minor axes.

Q: What is the equation of a parabola?

A: The equation of a parabola is a quadratic equation that can be written in the form y = ax^2 + bx + c, where a, b, and c are constants.

Q: How do I find the vertex of a parabola?

A: To find the vertex of a parabola, you can use the equation y = ax^2 + bx + c, where a, b, and c are constants.

Q: What is the equation of a hyperbola?

A: The equation of a hyperbola is a quadratic equation that can be written in the form ((x - h)^2 / a^2) - ((y - k)^2 / b^2) = 1, where (h, k) is the center of the hyperbola and a and b are the semi-major and semi-minor axes.

Q: How do I find the center and axes of a hyperbola?

A: To find the center and axes of a hyperbola, you can use the equation ((x - h)^2 / a^2) - ((y - k)^2 / b^2) = 1, where (h, k) is the center of the hyperbola and a and b are the semi-major and semi-minor axes.

Q: What is the equation of a rational function?

A: The equation of a rational function is a function that can be written in the form f(x) = p(x) / q(x), where p(x) and q(x) are polynomials.

Q: How do I find the domain of a rational function?

A: To find the domain of a rational function, you can use the equation f(x) = p(x) / q(x), where p(x) and q(x) are polynomials.

Q: What is the equation of a trigonometric function?

A: The equation of a trigonometric function is a function that can be written in the form f(x) = sin(x), cos(x), or tan(x), where x is the input.

Q: How do I find the range of a trigonometric function?

A: To find the range of a trigonometric function, you can use the equation f(x) = sin(x), cos(x), or tan(x), where x is the input.

Q: What is the equation of a logarithmic function?

A: The equation of a logarithmic function is a function that can be written in the form f(x) = log(x), where x is the input.

Q: How do I find the domain of a logarithmic function?

A: To find the domain of a logarithmic function, you can use the equation f(x) = log(x), where x is the input.

Q: What is the equation of an exponential function?

A: The equation of an exponential function is a function that can be written in the form f(x) = a^x, where a is the base and x is the input.

Q: How do I find the range of an exponential function?

A: To find the range of an exponential function, you can use the equation f(x) = a^x, where a is the base and x is the input.

Q: What is the equation of a power function?

A: The equation of a power function is a function that can be written in the form f(x) = x^n, where n is the exponent and x is the input.

Q: How do I find the domain of a power function?

A: To find the domain of a power function, you can use the equation f(x) = x^n, where n is the exponent and x is the input.

Q: What is the equation of a polynomial function?

A: The equation of a polynomial function is a function that can be written in the form f(x) = a_n x^n + a_(n-1) x^(n-1) + ... + a_1 x + a_0, where a_n, a_(n-1), ..., a_1, and a_0 are constants.

Q: How do I find the domain of a polynomial function?

A: To find the domain of a polynomial function, you can use the equation f(x) = a_n x^n + a_(n-1) x^(n-1) + ... + a_1 x + a_0, where a_n, a_(n-1), ..., a_1, and a_0 are constants.

Q: What is the equation of a rational polynomial function?

A: The equation of a rational polynomial function is a function that can be written in the form f(x) = p(x)