Solve

Definition

To solve a problem or equation means to find the value or values of the unknown variable(s) that satisfy the given conditions or make the equation true. Solving is a fundamental mathematical skill that involves using various strategies and techniques to determine the solution to a problem.

5 Must Know Facts For Your Next Test

1. Solving a formula for a specific variable involves isolating that variable on one side of the equation by performing inverse operations.
2. The goal when solving a formula is to express the variable of interest in terms of the other variables and constants in the equation.
3. Solving a formula often requires applying the order of operations, combining like terms, and using properties of equality to manipulate the equation.
4. Checking the solution by substituting the found value back into the original formula is an important step to verify the answer.
5. Solving formulas is a crucial skill for many real-world applications, such as in science, engineering, and finance.

Review Questions

• Explain the process of solving a formula for a specific variable.
  • To solve a formula for a specific variable, you need to isolate that variable on one side of the equation. This involves performing inverse operations, such as undoing addition by subtracting, undoing multiplication by dividing, etc. The goal is to manipulate the equation to express the variable of interest in terms of the other variables and constants in the formula. This may require applying the order of operations, combining like terms, and using properties of equality to simplify the expression until the desired variable is isolated.
• Describe the importance of checking the solution when solving a formula.
  • Checking the solution is a crucial step when solving a formula for a specific variable. After finding the value of the variable, it is important to substitute that value back into the original formula to verify that it satisfies the equation. This helps ensure that the solution is correct and that no mistakes were made during the solving process. Checking the solution also helps build confidence in the final answer and can identify any potential errors or special cases that may need to be considered.
• Analyze how solving formulas is applied in real-world situations.
  • Solving formulas is a fundamental skill that has numerous applications in the real world. In science, engineers and researchers use formulas to model physical phenomena and solve for unknown variables, such as calculating the force required to lift an object or determining the rate of a chemical reaction. In finance, professionals use formulas to calculate interest rates, loan payments, and investment returns. Solving formulas is also essential in fields like economics, physics, and computer science, where quantitative analysis and problem-solving are crucial. The ability to accurately solve for variables in formulas is a valuable skill that can be applied across a wide range of disciplines and real-world scenarios.

Related terms

Equation:

A mathematical statement that shows two expressions are equal, often containing one or more variables that need to be solved for.

Variable:

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

Inverse Operation:

An operation that 'undoes' another operation, allowing you to isolate a variable and solve for its value.