key term - Equal Sign

Definition

The equal sign (=) is a mathematical symbol used to indicate that two expressions or values are equivalent or have the same value. It is a fundamental concept in algebra that establishes a relationship of equality between the left and right sides of an equation.

5 Must Know Facts For Your Next Test

1. The equal sign indicates that the expressions on both sides of the equation have the same value and can be used interchangeably.
2. The properties of equality, such as the addition and subtraction properties, allow you to perform operations on both sides of an equation while maintaining the equality.
3. When solving systems of equations, the equal sign is used to represent the relationship between the variables and the constant terms.
4. The substitution method in solving systems of equations involves replacing one variable in one equation with an expression from another equation that has the same equal sign.
5. The elimination method in solving systems of equations involves adding or subtracting equations to eliminate one variable, using the equal sign to maintain the balance between the equations.

Review Questions

• Explain how the equal sign is used in the context of solving equations using the addition and subtraction properties of equality.
  • The equal sign is crucial when solving equations using the addition and subtraction properties of equality. These properties state that if you perform the same operation (addition or subtraction) on both sides of an equation, the equality will be maintained. For example, if you have the equation $x + 5 = 12$, you can subtract 5 from both sides to isolate the variable $x$, resulting in the equation $x = 7$. The equal sign ensures that the expressions on both sides of the equation remain equivalent throughout the solving process.
• Describe the role of the equal sign in the general strategy for solving linear equations.
  • The equal sign is central to the general strategy for solving linear equations. This strategy involves performing a series of steps, such as combining like terms, using the addition or subtraction properties of equality, and isolating the variable on one side of the equation. At each step, the equal sign is used to maintain the balance and ensure that the expressions on both sides of the equation remain equivalent. By manipulating the equation while preserving the equal sign, you can ultimately solve for the unknown variable.
• Analyze the significance of the equal sign in the context of solving systems of equations using the substitution and elimination methods.
  • In the context of solving systems of equations, the equal sign is crucial for both the substitution and elimination methods. When using the substitution method, the equal sign is used to represent the relationship between the variables in the equations, allowing you to replace one variable with an expression from another equation that has the same equal sign. In the elimination method, the equal sign is used to maintain the balance between the equations as you add or subtract them to eliminate a variable. The equal sign ensures that the system of equations remains equivalent throughout the solving process, enabling you to find the values of the variables that satisfy all the equations in the system.

Related terms

Equation:

A mathematical statement that expresses the equality of two expressions, typically involving variables and operations.

Algebraic Expression:

A combination of variables, numbers, and operations that represents a mathematical quantity.

Solve: To find the value(s) of the variable(s) that make an equation true.