Solving Equations

Definition

Solving equations is the process of finding the unknown value in an equation by performing mathematical operations to isolate the variable and determine its specific value. This is a fundamental skill in algebra that allows for the resolution of various types of equations, including those involving decimals.

5 Must Know Facts For Your Next Test

1. Solving equations with decimals involves the same principles as solving equations with whole numbers, but requires careful attention to decimal place values.
2. The goal when solving equations with decimals is to isolate the variable by performing inverse operations to both sides of the equation.
3. Decimal equations may require additional steps, such as moving the decimal point to convert decimals to whole numbers before performing operations.
4. Checking the solution by substituting the found value back into the original equation is an important step to ensure the equation is truly solved.
5. Solving decimal equations accurately is crucial for applications in real-world scenarios, such as personal finance, science, and engineering.

Review Questions

• Describe the general process for solving an equation with decimals.
  • To solve an equation with decimals, the first step is to identify the variable and isolate it on one side of the equation. This is typically done by performing inverse operations, such as adding, subtracting, multiplying, or dividing, to both sides of the equation. If necessary, the decimal values may need to be converted to whole numbers by moving the decimal point before performing the operations. Once the variable is isolated, the final step is to solve for the unknown value and check the solution by substituting it back into the original equation.
• Explain how the principles of solving equations with whole numbers apply to solving equations with decimals.
  • The fundamental principles of solving equations, such as performing inverse operations to isolate the variable and ensuring that the same operations are applied to both sides of the equation, are the same whether the equation involves whole numbers or decimals. The key difference is that when working with decimal equations, additional steps may be required to manage the decimal places, such as moving the decimal point to convert the values to whole numbers before performing operations. However, the overall goal and approach to solving the equation remains the same, regardless of the presence of decimal values.
• Discuss the importance of accurately solving equations with decimals in real-world applications.
  • Solving equations with decimals accurately is crucial in many real-world applications, as decimal values are commonly encountered in fields such as personal finance, science, and engineering. For example, in personal finance, the ability to solve equations involving decimals is essential for calculating interest rates, loan payments, and investment returns. In science, decimal equations are used to describe physical phenomena and to analyze experimental data. In engineering, decimal equations are used to design and analyze structures, systems, and processes. Inaccurate solutions to these decimal equations can lead to significant errors and potentially dangerous consequences. Therefore, the skill of solving equations with decimals is a fundamental and highly valuable mathematical competency in a wide range of practical applications.

Related terms

Variable: A symbol, usually a letter, that represents an unknown or changeable quantity in an equation.

Inverse Operations: Mathematical operations that undo each other, such as addition and subtraction or multiplication and division, used to isolate the variable in an equation.

Equation: A mathematical statement that expresses the equality of two expressions, with at least one variable.