Find The Value Of X X X If 4 ( X + 1 ) = 6 ( X − 3 4(x+1)=6(x-3 4 ( X + 1 ) = 6 ( X − 3 ]A. 11 B. 10 C. 8 D. 6 31. Simplify 8 Y + 2 6 − 12 Y − 10 24 \frac{8y+2}{6}-\frac{12y-10}{24} 6 8 Y + 2 ​ − 24 12 Y − 10 ​ A. 12 Y + 9 6 \frac{12y+9}{6} 6 12 Y + 9 ​ B. 12 Y − 9 24 \frac{12y-9}{24} 24 12 Y − 9 ​ C. 10 Y − 9 12 \frac{10y-9}{12} 12 10 Y − 9 ​ D.

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Introduction

Mathematics is a fundamental subject that plays a crucial role in our daily lives. It is used in various fields such as science, technology, engineering, and mathematics (STEM), economics, finance, and many more. In this article, we will focus on solving equations and simplifying expressions, which are essential skills in mathematics.

Solving Equations

Equations are statements that express the equality of two mathematical expressions. They can be linear or non-linear, and they can be solved using various methods such as algebraic manipulation, graphing, and numerical methods.

Example 1: Solving a Linear Equation

Let's consider the equation 4(x+1)=6(x−3)4(x+1)=6(x-3). Our goal is to find the value of xx that satisfies this equation.

To solve this equation, we can start by expanding the left-hand side of the equation:

4(x+1)=4x+44(x+1) = 4x + 4

Next, we can expand the right-hand side of the equation:

6(x−3)=6x−186(x-3) = 6x - 18

Now, we can set the two expressions equal to each other:

4x+4=6x−184x + 4 = 6x - 18

Subtracting 4x4x from both sides of the equation gives us:

4=2x−184 = 2x - 18

Adding 1818 to both sides of the equation gives us:

22=2x22 = 2x

Dividing both sides of the equation by 22 gives us:

x=11x = 11

Therefore, the value of xx that satisfies the equation 4(x+1)=6(x−3)4(x+1)=6(x-3) is x=11x = 11.

Simplifying Expressions

Simplifying expressions is an essential skill in mathematics that involves rewriting an expression in a simpler form. This can be done using various methods such as combining like terms, factoring, and canceling out common factors.

Example 2: Simplifying a Rational Expression

Let's consider the expression 8y+26−12y−1024\frac{8y+2}{6}-\frac{12y-10}{24}. Our goal is to simplify this expression.

To simplify this expression, we can start by finding a common denominator. In this case, the common denominator is 2424.

8y+26=(8y+2)(4)6(4)=32y+824\frac{8y+2}{6} = \frac{(8y+2)(4)}{6(4)} = \frac{32y+8}{24}

12y−1024\frac{12y-10}{24}

Now, we can subtract the two fractions:

32y+824−12y−1024=32y+8−12y+1024\frac{32y+8}{24} - \frac{12y-10}{24} = \frac{32y+8-12y+10}{24}

Combining like terms gives us:

20y+1824\frac{20y+18}{24}

Dividing both the numerator and the denominator by 22 gives us:

10y+912\frac{10y+9}{12}

Therefore, the simplified form of the expression 8y+26−12y−1024\frac{8y+2}{6}-\frac{12y-10}{24} is 10y+912\frac{10y+9}{12}.

Conclusion

Solving equations and simplifying expressions are essential skills in mathematics that are used in various fields such as science, technology, engineering, and mathematics (STEM), economics, finance, and many more. In this article, we have discussed how to solve linear equations and simplify rational expressions using various methods such as algebraic manipulation, graphing, and numerical methods. We have also provided examples of how to solve equations and simplify expressions, and we have shown that with practice and patience, anyone can become proficient in these skills.

Final Answer

The final answer to the first question is:

  • x=11x = 11

The final answer to the second question is:

  • 10y+912\frac{10y+9}{12}

Introduction

Mathematics is a fundamental subject that plays a crucial role in our daily lives. It is used in various fields such as science, technology, engineering, and mathematics (STEM), economics, finance, and many more. In this article, we will focus on solving equations and simplifying expressions, which are essential skills in mathematics.

Q&A: Solving Equations

Q: What is an equation?

A: An equation is a statement that expresses the equality of two mathematical expressions. It can be linear or non-linear, and it can be solved using various methods such as algebraic manipulation, graphing, and numerical methods.

Q: How do I solve a linear equation?

A: To solve a linear equation, you can start by expanding the left-hand side of the equation and then setting it equal to the right-hand side. You can then use algebraic manipulation to isolate the variable and solve for its value.

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 solving an equation. 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 simplify an expression?

A: To simplify an expression, you can start by combining like terms, factoring, and canceling out common factors. You can also use algebraic manipulation to rewrite the expression in a simpler form.

Q: What is a rational expression?

A: A rational expression is a fraction that contains variables in the numerator or denominator. It can be simplified by finding a common denominator and combining like terms.

Q&A: Simplifying Expressions

Q: How do I simplify a rational expression?

A: To simplify a rational expression, you can start by finding a common denominator and combining like terms. You can also use algebraic manipulation to rewrite the expression in a simpler form.

Q: What is the difference between a rational expression and a rational number?

A: A rational number is a number that can be expressed as the ratio of two integers. A rational expression is a fraction that contains variables in the numerator or denominator.

Q: How do I add or subtract rational expressions?

A: To add or subtract rational expressions, you can start by finding a common denominator and combining like terms. You can also use algebraic manipulation to rewrite the expression in a simpler form.

Q: What is the final answer to the expression 8y+26−12y−1024\frac{8y+2}{6}-\frac{12y-10}{24}?

A: The final answer to the expression 8y+26−12y−1024\frac{8y+2}{6}-\frac{12y-10}{24} is 10y+912\frac{10y+9}{12}.

Conclusion

Solving equations and simplifying expressions are essential skills in mathematics that are used in various fields such as science, technology, engineering, and mathematics (STEM), economics, finance, and many more. In this article, we have discussed how to solve linear equations and simplify rational expressions using various methods such as algebraic manipulation, graphing, and numerical methods. We have also provided examples of how to solve equations and simplify expressions, and we have shown that with practice and patience, anyone can become proficient in these skills.

Final Answer

The final answer to the first question is:

  • x=11x = 11

The final answer to the second question is:

  • 10y+912\frac{10y+9}{12}