In Exercises 117–130, simplify each algebraic expression. 7x+5x

Verified step by step guidance

1. Identify like terms in the expression: 7x and 5x are like terms because they both contain the variable x.
2. Combine the coefficients of the like terms: Add the coefficients 7 and 5 together.
3. Write the simplified expression by multiplying the sum of the coefficients by the common variable x.
4. The expression is now simplified to a single term with the variable x.
5. Ensure that the expression is in its simplest form with no further like terms to combine.

Key Concepts

Combining Like Terms

Combining like terms is a fundamental algebraic process where terms with the same variable and exponent are added or subtracted. In the expression 7x + 5x, both terms are 'like' because they contain the variable x raised to the first power. This allows us to simplify the expression by adding the coefficients (7 and 5) together.

Coefficients

Coefficients are the numerical factors that multiply the variables in algebraic expressions. In the expression 7x + 5x, the coefficients are 7 and 5. Understanding coefficients is essential for simplifying expressions, as they determine how many units of the variable are present in each term.

Algebraic Expressions

Algebraic expressions are combinations of numbers, variables, and operations that represent a value. They can include constants, coefficients, and various mathematical operations. Simplifying algebraic expressions, like 7x + 5x, is a key skill in algebra that helps in solving equations and understanding mathematical relationships.