Define number sentence.
A mathematical statement that includes numbers and operations but does not have an equality sign.
Define equation.
A mathematical statement that asserts the equality of two expressions, containing an equality sign.
True or false: A number sentence can be an equation.
FALSE
A number sentence lacks an equality sign, distinguishing it from an equation.
What does a solution of an equation represent?
A value that makes the equation true when substituted for the variable.
Fill in the blank: An equation can have _______ solutions.
One, none, or infinitely many
True or false: Every equation has a solution.
FALSE
Some equations, like x + 1 = x, have no solutions.
What is the goal when solving an equation?
To find the value of the variable that satisfies the equation.
Fill in the blank: A variable in an equation represents _______.
An unknown value
Define solution set.
The set of all possible solutions to an equation.
What is a true statement in relation to equations?
A statement that holds true when the variable is replaced with its solution.
Fill in the blank: An equation is balanced when both sides are _______.
Equal
True or false: A number sentence can be solved.
FALSE
Number sentences do not have an equality to solve for a variable.
What does it mean if an equation has no solution?
There is no value for the variable that can satisfy the equation.
Fill in the blank: The left side of an equation is equal to the _______.
Right side
Define identity in equations.
An equation that is true for all values of the variable.
What is the first step in solving an equation?
Isolate the variable on one side of the equation.
Fill in the blank: An equation can be represented as A = B, where A and B are _______.
Expressions
True or false: The solution of an equation is always a single number.
FALSE
Some equations can have multiple solutions or none.
What is a linear equation?
An equation that graphs as a straight line and has a degree of one.
Fill in the blank: The solution of the equation 2x + 3 = 7 is _______.
x = 2
Define algebraic equation.
An equation that includes one or more variables and constants.
What does it mean for an equation to be consistent?
It has at least one solution.
Fill in the blank: A distributive property helps simplify equations by _______.
Multiplying a single term across terms inside parentheses
True or false: Every number sentence can be converted into an equation.
TRUE
By adding an equality sign and an expression to balance it.
