What is the first step to solve the equation 5x - 12 = 58?

Add 12 to both sides of the equation to isolate the term with x: 5x = 58 + 12.

How do you solve for x in the equation 5x = 70?

Divide both sides by 5: x = 70 ÷ 5.

Is the solution x = 14 correct for the equation 5x - 12 = 58?

Yes, substituting x = 14 back into the original equation satisfies it.

How can I check my solution for the equation 5x - 12 = 58?

Plug x = 14 into the original equation and verify that both sides are equal.

Can this equation be solved by graphing?

Yes, by graphing y = 5x - 12 and y = 58, their intersection point gives the solution x = 14.

What type of equation is 5x - 12 = 58?

It is a linear equation in one variable.

What does the solution x = 14 tell us in the context of this equation?

It indicates the value of x that makes the equation true.

Are there any other solutions to 5x - 12 = 58?

No, since it's a linear equation, it has only one solution: x = 14.

Do You Know This?5x-12=58

Do You Know This? 5x - 12 = 58

Mathematics is an essential part of our daily lives, from simple calculations to complex problem-solving. One of the fundamental concepts in algebra involves solving equations like 5x - 12 = 58. Understanding how to solve such equations not only enhances your math skills but also improves your logical thinking and problem-solving abilities. In this comprehensive guide, we will explore the steps to solve the equation 5x - 12 = 58, discuss related concepts, and provide tips to master similar problems.

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Understanding the Equation 5x - 12 = 58

Before diving into the solution, it’s important to understand what the equation represents and the basic components involved.

Breaking Down the Equation

5x: This is a term where 5 is multiplied by the variable x.
-12: This is a constant term subtracted from 5x.
= 58: The equation states that the expression on the left equals 58.

In essence, the goal is to find the value of x that makes the equation true.

The Basic Structure of Linear Equations

The equation 5x - 12 = 58 is a linear algebraic equation, meaning it involves variables to the first power only. These equations generally have the form ax + b = c, where a, b, and c are constants, and x is the variable to solve for.

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Step-by-Step Solution to 5x - 12 = 58

To find the value of x, follow systematic steps that isolate x on one side of the equation.

Step 1: Add 12 to both sides

The first step involves moving constant terms to the other side to isolate the term with the variable.

Equation: 5x - 12 = 58

Add 12 to both sides:

5x - 12 + 12 = 58 + 12

Simplify:

5x = 70

Step 2: Divide both sides by 5

Next, divide both sides of the equation by the coefficient of x (which is 5) to solve for x.

5x / 5 = 70 / 5

Simplify:

x = 14

Final Answer:

x = 14

This is the solution to the equation 5x - 12 = 58.

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Verifying Your Solution

Always verify your solution by substituting the value back into the original equation.

Original equation: 5x - 12 = 58

Substitute x = 14:

5(14) - 12 = ?

Calculate:

70 - 12 = 58

Result:

58 = 58

Since both sides are equal, x = 14 is the correct solution.

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Related Concepts and Tips for Solving Algebraic Equations

Understanding the solution process for 5x - 12 = 58 can be extended to various other algebra problems.

1. Handling Equations with Multiple Variables

While this problem involves a single variable, more complex equations may include multiple variables. Strategies include:

Isolating one variable at a time.

Using substitution or elimination methods for systems of equations.

2. Working with Inequalities

The techniques used here also apply to inequalities like 5x - 12 > 58 or 5x - 12 ≤ 58. Pay attention to the inequality signs during operations.

3. Common Mistakes to Avoid

Forgetting to perform the same operation on both sides.
Incorrectly handling negative signs.
Dividing by zero (ensure the coefficient of the variable is not zero).

4. Practice Problems

To strengthen your algebra skills, try solving similar equations:

3x + 7 = 22

4x - 5 = 15

2(3x - 4) = 10

6x / 2 = 9

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Applications of Solving Equations in Real Life

Mastering algebraic equations like 5x - 12 = 58 has practical applications across various fields.

1. Financial Planning

Calculating interest, loan payments, or budgeting often involves solving equations.

2. Engineering and Science

Designing structures, analyzing data, and solving physics problems frequently require algebraic solutions.

3. Computer Programming

Algorithms and code logic depend on solving equations and inequalities efficiently.

4. Everyday Problem Solving

From adjusting recipes to calculating travel time, algebraic thinking is useful in daily tasks.

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Conclusion: Do You Know How to Solve 5x - 12 = 58?

Understanding how to solve the equation 5x - 12 = 58 is a fundamental skill in algebra. By following straightforward steps—adding 12 to both sides and then dividing by 5—you can quickly find that x = 14. Always verify your solutions to ensure accuracy, and apply the same principles to more complex equations. Developing proficiency in solving such equations enhances your overall mathematical literacy, which is invaluable across many domains in academics, careers, and everyday life.

Remember: Practice makes perfect. Keep solving different types of equations to build confidence and improve your problem-solving skills. Whether you're a student, educator, or lifelong learner, mastering these concepts opens the door to more advanced mathematics and logical thinking.

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