Algebraic Expressions: Key Concepts

• Key concepts for algebraic expressions

Selected Response

• The expression w + 8 can be described as "the sum of w and 8"
• It can also be described as "w plus 8".
• If Wilkie makes w dollars per hour and Jonah makes $2 less, Jonah's pay is represented by w - 2.
• Appropriate ways to write "six times t" include 6 x t and 6t.
• The value of 6x - 4 when x = -5 is -34
• The value of the expression (5a + b) / (-2ac) when a = 4, b = 12, and c = -1 is 4
• The value that correctly fills in the blank in the equation 5(3x - 2) = blank is 15x - 10.
• Expressions equivalent to 5(t - 2) include 5t - 10 and 4(t - 2) + t - 2.
• The factored form of 8x - 28 using the greatest common factor is 4(2x - 7).
• Expressions equivalent to 6m + 4 - 2m + 9 include 4m + 13 and 4(m + 2) + 5.
• The expression equivalent to 6(5x - 2) + 2 is 30x - 10.

Constructed Response

• "Four less than p" can be written as p - 4.
• "The quotient of m and 2" is m / 2.
• "5x" can be described as "5 times x" or "the product of 5 and x".
• "6k + 1" is described as "one more than the product of 6 and k" or "6 times k plus 1".
• 9h - 4 when h = 3 evaluates to 23.
• 3(a - 6) when a = 8 evaluates to 6.
• -10w + (n / 4) when n = 60 and w = -4 evaluates to 25.
• (ad)² / (3d + 2) when a = 1 and d = -6 evaluates to -2 1/4.
• If Karen purchased x apples for y dollars and each apple costs $0.60, then 0.60x = y.
  • One possible set of values is x = 5 and y = 3.
  • Another is x = 10 and y = 6.

Simplify Expressions

• 8 + 6b - b + 4 simplifies to 5b + 12.
• 9(a + 6) simplifies to 9a + 54.
• 2(5k - 3) - 10 simplifies to 10k - 16.
• 12 + (3 / 4)(x + 12) + (1 / 4)x simplifies to 21 + x.

Factoring Expressions

• The factored form of 6x + 24 using the greatest common factor is 6(x + 4).
• The factored form of 8x - 20 using the greatest common factor is 4(2x - 5).