Translate The Following Sentence Into An Equation. Then Solve The Equation.Five Times A Number, Added To 9, Is 39. Find The Number.

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Introduction

Equations are a fundamental concept in mathematics, and solving them is a crucial skill for anyone interested in mathematics, science, or engineering. In this article, we will translate a given sentence into an equation and then solve the equation to find the unknown number.

Translating the Sentence into an Equation

The given sentence is: "Five times a number, added to 9, is 39."

To translate this sentence into an equation, we need to follow the order of operations (PEMDAS):

  1. Identify the unknown number: Let's call the unknown number "x".
  2. Translate the sentence into an equation:
    • "Five times a number" can be translated to 5x.
    • "Added to 9" can be translated to +9.
    • "Is 39" can be translated to = 39.
  3. Combine the translated parts into a single equation: 5x + 9 = 39.

Solving the Equation

Now that we have the equation, we can solve for the unknown number "x". To do this, we need to isolate the variable "x" on one side of the equation.

Step 1: Subtract 9 from both sides

Subtracting 9 from both sides of the equation will help us get rid of the constant term on the left side:

5x + 9 - 9 = 39 - 9 5x = 30

Step 2: Divide both sides by 5

Now that we have the equation 5x = 30, we can divide both sides by 5 to solve for "x":

(5x) / 5 = 30 / 5 x = 6

Conclusion

In this article, we translated a given sentence into an equation and then solved the equation to find the unknown number. The equation was 5x + 9 = 39, and we solved for "x" by subtracting 9 from both sides and then dividing both sides by 5. The final answer is x = 6.

Real-World Applications

Solving equations is a crucial skill in many real-world applications, such as:

  • Science: Equations are used to model real-world phenomena, such as the motion of objects, the behavior of electrical circuits, and the growth of populations.
  • Engineering: Equations are used to design and optimize systems, such as bridges, buildings, and electronic circuits.
  • Economics: Equations are used to model economic systems, such as supply and demand, inflation, and unemployment.

Tips and Tricks

Here are some tips and tricks to help you solve equations:

  • Read the problem carefully: Make sure you understand what the problem is asking for.
  • Identify the unknown variable: Make sure you know what the unknown variable is and what it represents.
  • Use the order of operations: Follow the order of operations (PEMDAS) to simplify the equation.
  • Isolate the variable: Get the variable on one side of the equation by adding, subtracting, multiplying, or dividing both sides by the same value.

Common Mistakes

Here are some common mistakes to avoid when solving equations:

  • Not reading the problem carefully: Make sure you understand what the problem is asking for.
  • Not identifying the unknown variable: Make sure you know what the unknown variable is and what it represents.
  • Not following the order of operations: Make sure you follow the order of operations (PEMDAS) to simplify the equation.
  • Not isolating the variable: Make sure you get the variable on one side of the equation by adding, subtracting, multiplying, or dividing both sides by the same value.

Conclusion

Introduction

In our previous article, we discussed how to translate a given sentence into an equation and then solve the equation to find the unknown number. 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 two mathematical expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS). The LHS is the expression on the left side of the equation, and the RHS is the expression on the right side.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when simplifying an expression. The acronym PEMDAS is commonly used to remember the order of operations:

  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 linear equation?

A: To solve a linear equation, follow these steps:

  1. Isolate the variable: Get the variable on one side of the equation by adding, subtracting, multiplying, or dividing both sides by the same value.
  2. Simplify the equation: Simplify the equation by combining like terms.
  3. Check your solution: Check your solution by plugging it back into the original equation.

Q: What is a quadratic equation?

A: A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable is two. It has the general form ax^2 + bx + c = 0, where a, b, and c are constants.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you can use the following methods:

  1. Factoring: If the quadratic expression can be factored, you can set each factor equal to zero and solve for the variable.
  2. Quadratic formula: If the quadratic expression cannot be factored, you can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a.
  3. Graphing: You can also graph the quadratic function and find the x-intercepts.

Q: What is a system of equations?

A: A system of equations is a set of two or more equations that have the same variables. To solve a system of equations, you can use the following methods:

  1. Substitution: Substitute one equation into the other equation to eliminate one variable.
  2. Elimination: Add or subtract the equations to eliminate one variable.
  3. Graphing: Graph the equations on a coordinate plane and find the point of intersection.

Q: How do I solve a system of equations?

A: To solve a system of equations, follow these steps:

  1. Choose a method: Choose a method to solve the system of equations, such as substitution, elimination, or graphing.
  2. Solve the system: Solve the system of equations using the chosen method.
  3. Check your solution: Check your solution by plugging it back into the original equations.

Conclusion

Solving equations is a crucial skill in mathematics, science, and engineering. By following the steps outlined in this article, you can answer frequently asked questions about solving equations and become more confident in your ability to solve equations. Remember to practice solving equations regularly to improve your skills.