Equivalent expressions are always equal to each other. If the expressions have variables, they are equal whenever the same value is used for the variable in each expression.

For example, \(3x+4x\) is equivalent to \(5x+2x\).

• When \(x\) is 3, both expressions equal 21.
• When \(x\) is 10, both expressions equal 70.
• When \(x\) is any other number, both expressions still have equal value.

A solution to an equation is a number that can be used in place of the variable to make the equation true.

• The solution to the equation \(m+1=8\) is 7, because it is true that \(7+1=8\).
• The solution to \(m+1=8\) is not 9, because \(9+1\) does not equal 8. 

A term is a part of an expression. It can be a single number, a variable, or a number and a variable that are multiplied together.

• 7, \(y\), and \(9a\) are examples of terms.
• The expression \(5x+3\) has 2 terms: \(5x\) and \(3\).

A variable is a letter that represents a number. Different numbers can be chosen for the value of the variable.

In the expression \(10-x\), the variable is \(x\).

• If the value of \(x\) is 3, then \(10-x=7\), because \(10-3=7\).
• If the value of \(x\) is 6, then \(10-x=4\), because \(10-6=4\).