Section 1.3 The Order of Operations, Algebraic Expressions, and Equations 33 Many of the problems that we encounter in math require us to have the ability to express mathematical relationships correctly. Example 5 practices this skill. When one of the numbers is not known, a variable is used to represent this unknown number. �� ������������������������ ������������������ Translate each phrase into an algebraic expression, equation, or inequality. Use the variable �� to represent the unknown number. Problems Solutions 5a. A number increased by 7 Since “increase” means add, the expression is x + 7 5b. Five less than a number Since “less than” means subtract, the expression is x − 5 5c. The difference of a number and 2 Since “difference” means subtract, the expression is x − 2 5d. The product of 5 and a number Since “product” means multiply, the expression is 5 · x or 5x 5e. The quotient of a number and 3 Since “quotient” means divide, the expression is x 3 5f. The sum of twice a number and 4 Since “twice a number” means multiply and “sum” means add, the expression is 2x + 4 5g. The difference of three times a number and 1 Since “three times” means multiply and “difference” means subtract, the expression is 3x − 1 5h. Twice the sum of a number and 6 Since “sum” means add and “twice” means multiply, we have 2(x + 6) 5i. Three less than one-half of a number Since “less than” means subtract and “ 1 2 of ” means multiply we have 1 2 x - 3 5j. A number less than 8 is the same as three times the number. Since “is the same as” means equal to, the translation is an equation of the form 8 − x = 3x 5k. A number is less than 3. Since “is less than” denotes inequality, we have x < 3 Student Check 5 Translate each phrase or sentence into an algebraic expression, equation, or inequality. Use the variable x to represent the unknown number. a. A number decreased by 2 b. Three more than a number c. The sum of three times a number and 5 d. The quotient of a number and 2 e. The difference of a number and 4 f. The product of a number and 6 g. The difference of twice a number and 9 h. Three times the sum of a number and 1 i. Five less than one-third of a number j. One more than four times a number is 15. k. Twice a number is less than 4.
hendricks_beginning_algebra_1e_ch1_3
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