Equation Solving Strategies

Definition

Equation solving strategies refer to the systematic methods and techniques used to find the unknown value(s) in an equation. These strategies involve the application of the properties of equality to isolate the variable and determine the solution to the equation.

5 Must Know Facts For Your Next Test

1. The goal of equation solving strategies is to isolate the variable on one side of the equation by performing inverse operations on both sides.
2. Applying the addition and subtraction properties of equality are fundamental steps in solving linear equations.
3. Combining like terms on each side of the equation can simplify the equation and make it easier to solve.
4. Checking the solution by substituting the found value back into the original equation is an important step to verify the accuracy of the solution.
5. Equation solving strategies can be extended to solve more complex equations, such as those involving multiple variables or nonlinear expressions.

Review Questions

• Explain how the addition and subtraction properties of equality are used to solve linear equations.
  • The addition and subtraction properties of equality allow you to isolate the variable on one side of the equation by performing inverse operations on both sides. For example, to solve an equation like $2x + 5 = 11$, you would first subtract 5 from both sides to isolate the $2x$ term, resulting in $2x = 6$. Then, you would divide both sides by 2 to solve for $x$, arriving at the solution $x = 3$. By applying these properties systematically, you can solve for the unknown variable in a linear equation.
• Describe the process of verifying the solution to an equation by substitution.
  • Verifying the solution to an equation by substitution involves taking the value you found for the variable and substituting it back into the original equation. This allows you to check if the equation is still true when the variable is replaced by the solution. For example, if you solved the equation $2x + 5 = 11$ and found that $x = 3$, you would substitute 3 for $x$ in the original equation: $2(3) + 5 = 11$. If the equation is still true, then you have correctly solved for the variable, and the solution is valid.
• Analyze how equation solving strategies can be extended to solve more complex equations, such as those involving multiple variables or nonlinear expressions.
  • Equation solving strategies can be extended to solve more complex equations by applying the same principles of isolating variables and using inverse operations, but with additional steps and considerations. For equations with multiple variables, you would need to solve for one variable at a time, treating the other variables as constants. For nonlinear equations, such as those involving exponents or polynomials, you may need to use more advanced techniques like factoring, completing the square, or applying the quadratic formula. The core idea of systematically isolating the variable remains the same, but the specific steps required become more sophisticated to handle the increased complexity of the equation.

Related terms

Addition Property of Equality: The principle that allows the same quantity to be added to both sides of an equation without changing the equality.

Subtraction Property of Equality: The principle that allows the same quantity to be subtracted from both sides of an equation without changing the equality.

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