X+3x +2x+5° =180° X + 3 X + 2 X + 5 = 180 X + 3x + 2x + 5 = 18 0 X + 3 X + 2 X + 5 = 180 ​

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Solving the Equation: X+3x +2x+5° =180°

In this article, we will delve into the world of algebra and explore a simple yet intriguing equation: X+3x +2x+5° =180°. This equation may seem straightforward, but it requires a clear understanding of algebraic expressions and the rules of arithmetic operations. We will break down the equation step by step, and by the end of this article, you will have a solid grasp of how to solve it.

Understanding the Equation

The given equation is X+3x +2x+5° =180°. At first glance, it may seem like a simple addition problem, but it's essential to recognize that we are dealing with algebraic expressions. The variable X is represented by a single letter, and the coefficients (3, 2, and 5) are numbers that multiply the variable.

Combining Like Terms

To simplify the equation, we need to combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have three terms with the variable X: X, 3x, and 2x. We can combine these terms by adding their coefficients.

X + 3x + 2x = (1 + 3 + 2)x = 6x

Now, the equation becomes 6x + 5° = 180°.

Isolating the Variable

Our goal is to isolate the variable X. To do this, we need to get rid of the constant term (5°) on the left side of the equation. We can do this by subtracting 5° from both sides of the equation.

6x + 5° = 180°
6x = 180° - 5°
6x = 175°

Solving for X

Now that we have isolated the variable X, we can solve for its value. To do this, we need to divide both sides of the equation by 6.

6x = 175°
x = 175° / 6
x = 29.17°

Conclusion

In this article, we have solved the equation X+3x +2x+5° =180° step by step. We combined like terms, isolated the variable X, and finally solved for its value. The solution to the equation is x = 29.17°. This equation may seem simple, but it requires a clear understanding of algebraic expressions and the rules of arithmetic operations.

Frequently Asked Questions

  • What is the value of X in the equation X+3x +2x+5° =180°?
  • How do you combine like terms in an algebraic expression?
  • What is the rule for isolating a variable in an equation?

Answers

  • The value of X in the equation X+3x +2x+5° =180° is 29.17°.
  • To combine like terms, you add the coefficients of the terms with the same variable raised to the same power.
  • To isolate a variable, you need to get rid of the constant term on the left side of the equation by subtracting it from both sides.

Further Reading

If you want to learn more about algebra and solving equations, here are some recommended resources:

  • Khan Academy: Algebra
  • Mathway: Algebra Solver
  • Wolfram Alpha: Algebra Calculator

References

  • "Algebra" by Michael Artin
  • "Introduction to Algebra" by Richard Rusczyk
  • "Algebra and Trigonometry" by James Stewart
    Frequently Asked Questions: X+3x +2x+5° =180°

In this article, we will address some of the most common questions related to the equation X+3x +2x+5° =180°. Whether you are a student, a teacher, or simply someone who wants to learn more about algebra, this article is for you.

Q: What is the value of X in the equation X+3x +2x+5° =180°?

A: The value of X in the equation X+3x +2x+5° =180° is 29.17°. To find this value, we need to combine like terms, isolate the variable X, and finally solve for its value.

Q: How do you combine like terms in an algebraic expression?

A: To combine like terms, you add the coefficients of the terms with the same variable raised to the same power. In the equation X+3x +2x+5° =180°, we have three terms with the variable X: X, 3x, and 2x. We can combine these terms by adding their coefficients.

X + 3x + 2x = (1 + 3 + 2)x = 6x

Q: What is the rule for isolating a variable in an equation?

A: To isolate a variable, you need to get rid of the constant term on the left side of the equation by subtracting it from both sides. In the equation 6x + 5° = 180°, we can isolate the variable X by subtracting 5° from both sides.

6x + 5° = 180°
6x = 180° - 5°
6x = 175°

Q: How do you solve for the value of a variable in an equation?

A: To solve for the value of a variable, you need to isolate the variable and then divide both sides of the equation by the coefficient of the variable. In the equation 6x = 175°, we can solve for the value of X by dividing both sides of the equation by 6.

6x = 175°
x = 175° / 6
x = 29.17°

Q: What is the difference between a coefficient and a constant in an algebraic expression?

A: A coefficient is a number that multiplies a variable in an algebraic expression. A constant is a number that does not have a variable associated with it. In the equation X+3x +2x+5° =180°, the coefficients are 1, 3, and 2, and the constant is 5°.

Q: How do you simplify an algebraic expression?

A: To simplify an algebraic expression, you need to combine like terms and eliminate any unnecessary parentheses or brackets. In the equation X+3x +2x+5° =180°, we can simplify the expression by combining the like terms X, 3x, and 2x.

X + 3x + 2x = (1 + 3 + 2)x = 6x

Q: What is the order of operations in algebra?

A: The order of operations in algebra is Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction (PEMDAS). This means that you need to evaluate expressions inside parentheses first, followed by exponents, then multiplication and division, and finally addition and subtraction.

Q: How do you evaluate an expression with multiple variables?

A: To evaluate an expression with multiple variables, you need to substitute the values of the variables into the expression and then simplify. For example, if we have the expression 2x + 3y and we know that x = 4 and y = 5, we can substitute these values into the expression and simplify.

2x + 3y = 2(4) + 3(5)
= 8 + 15
= 23

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. A quadratic equation is an equation in which the highest power of the variable is 2. For example, the equation 2x + 3 = 5 is a linear equation, while the equation x^2 + 2x + 1 = 0 is a quadratic equation.

Q: How do you solve a quadratic equation?

A: To solve a quadratic equation, you need to use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. This formula will give you two solutions for the value of x. For example, if we have the quadratic equation x^2 + 2x + 1 = 0, we can use the quadratic formula to find the solutions.

x = (-2 ± √(2^2 - 4(1)(1))) / 2(1)
= (-2 ± √(4 - 4)) / 2
= (-2 ± √0) / 2
= (-2 ± 0) / 2
= -1

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

A: A rational expression is an expression that can be written as the ratio of two polynomials. An irrational expression is an expression that cannot be written as the ratio of two polynomials. For example, the expression 2x / (x + 1) is a rational expression, while the expression √x is an irrational expression.

Q: How do you simplify a rational expression?

A: To simplify a rational expression, you need to factor the numerator and denominator and then cancel out any common factors. For example, if we have the rational expression 2x / (x + 1), we can simplify it by factoring the numerator and denominator.

2x / (x + 1) = (2x) / (x + 1)
= 2x / (x + 1) × (x - 1) / (x - 1)
= (2x(x - 1)) / ((x + 1)(x - 1))
= 2x(x - 1) / (x^2 - 1)
= 2x(x - 1) / ((x + 1)(x - 1))
= 2x / (x + 1)

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

A: A polynomial is an expression that consists of variables and coefficients combined using only addition, subtraction, and multiplication. A rational expression is an expression that can be written as the ratio of two polynomials. For example, the expression 2x^2 + 3x + 1 is a polynomial, while the expression 2x / (x + 1) is a rational expression.

Q: How do you evaluate a polynomial expression?

A: To evaluate a polynomial expression, you need to substitute the values of the variables into the expression and then simplify. For example, if we have the polynomial expression 2x^2 + 3x + 1 and we know that x = 4, we can substitute this value into the expression and simplify.

2x^2 + 3x + 1 = 2(4)^2 + 3(4) + 1
= 2(16) + 12 + 1
= 32 + 12 + 1
= 45

Q: What is the difference between a linear inequality and a quadratic inequality?

A: A linear inequality is an inequality in which the highest power of the variable is 1. A quadratic inequality is an inequality in which the highest power of the variable is 2. For example, the inequality 2x + 3 > 5 is a linear inequality, while the inequality x^2 + 2x + 1 < 0 is a quadratic inequality.

Q: How do you solve a linear inequality?

A: To solve a linear inequality, you need to isolate the variable and then determine the direction of the inequality. For example, if we have the linear inequality 2x + 3 > 5, we can isolate the variable x by subtracting 3 from both sides.

2x + 3 > 5
2x > 5 - 3
2x > 2
x > 1

Q: How do you solve a quadratic inequality?

A: To solve a quadratic inequality, you need to use the quadratic formula to find the solutions to the corresponding quadratic equation, and then determine the direction of the inequality. For example, if we have the quadratic inequality x^2 + 2x + 1 < 0, we can use the quadratic formula to find the solutions to the corresponding quadratic equation.

x^2 + 2x + 1 = 0
x = (-2 ± √(2^2 - 4(1)(1))) / 2(1)
= (-2 ± √(4 - 4)) / 2
= (-2 ± √0) / 2
= (-2 ± 0) / 2
= -1

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

A: A system of linear equations is a set of two or more linear equations that are solved simultaneously. A system of quadratic equations is a set of two or more quadratic equations that