# True and False Equations

Examples, solutions, and videos to help Algebra I students understand that an equation is a statement of equality between two expressions.

### New York State Common Core Math Algebra I, Module 1, Lesson 10

Student Outcomes
Students understand that an equation is a statement of equality between two expressions. When values are substituted for the variables in an equation, the equation is either true or false. Students find values to assign to the variables in equations that make the equations true statements.

Definitions
A number sentence is a statement of equality between two numerical expressions.
A number sentence is said to be true if both numerical expressions are equivalent (that is, both evaluate to the same number). It is said to be false otherwise. True and false are called truth values.

An algebraic equation is a statement of equality between two expressions.
Algebraic equations can be number sentences (when both expressions are numerical), but often they contain symbols whose values have not been determined.

Exit Ticket

1. Consider the following equation, where represents a real number: √(a+1) = √a + 1.
Is this statement a number sentence? If so, is the sentence TRUE or FALSE?
2. Suppose we are told that b has the value 4. Can we determine whether the equation below is TRUE or FALSE? If so, say which it is, if not, state that it cannot be determined. Justify your answer. √(b+1) = √b + 1
3. For what value of is the following equation TRUE?
√(c+1) = √c + 1

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.