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.

To expand an expression, use the distributive property to rewrite a product as a sum. The new expression is equivalent to the original expression.

For example, the expression \(5(4x+7)\) can be expanded to get the equivalent expression \(20x + 35\).

To factor an expression, use the distributive property to rewrite a sum as a product. The new expression is equivalent to the original expression.

For example, the expression \(20x + 35\) can be factored to get the equivalent expression \(5(4x+7)\).

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

• A solution to the inequality \(c<10\) is 5, because it is true that \(5<10\).
• Some other solutions to this inequality are 9.9, 0, and -4.

Terms are the parts of an expression that are added together. They 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 \(5x+3-18\) has 3 terms: \(5x\), 3, and -18.