Basic Algebra Substitution Flashcards

Algebra Substitution Overview

• Substitution in algebra involves replacing variables (e.g., x) with given numerical values.
• For instance, if x=6 in the expression x − 2, it becomes 6 − 2 = 4.

Simple Examples of Substitution

• If x=2, substitute into 10/x + 4:
  • 10/2 + 4 = 5 + 4 = 9.
• Substitute x=5 into x + x/2:
  • 5 + 5/2 = 5 + 2.5 = 7.5.
• With x=3 and y=4, evaluate x^2 + xy:
  • 3^2 + 3×4 = 9 + 12 = 21.
• With x=3 and unknown y, evaluate x^2 + xy:
  • 3^2 + 3y = 9 + 3y (y remains unknown).

Negative Numbers in Substitution

• Use parentheses for negative numbers to ensure proper calculations.
• With x = −2 in 1 − x + x^2:
  • 1 − (−2) + (−2)^2 = 1 + 2 + 4 = 7.

Rules for Operations

• Adding/Subtracting:
  • Two like signs become positive; e.g., 3+(+2) = 5.
  • Two unlike signs yield a negative; e.g., 7 + (−2) = 5.
• Multiplying/Dividing:
  • Two like signs yield a positive; e.g., (−3) × (−2) = 6.
  • Two unlike signs yield a negative; e.g., 3 × (−2) = −6.

Evaluating Expressions with Given Values

• If x=4, find 12/x + 3:
  • 12/4 + 3 = 3 + 3 = 6.
• If y=10, evaluate 5(y-4)/2:
  • 5(10-4)/2 = 5×6/2 = 30/2 = 15.
• With x=2 and y=3, calculate xy + y²:
  • 2×3 + 3² = 6 + 9 = 15.
• With x=5 and y=6, evaluate 2x - 12/y:
  • 2×5 - 12/6 = 10 - 2 = 8.
• If x=4 and y=2, evaluate x² + y³:
  • (4×4) + (2×2×2) = 16 + 8 = 24.
• For z = -3, find z² - z - 1:
  • (-3)² - (-3) - 1 = 9 + 3 - 1 = 11.
• If y = -5, evaluate 3y² + 7y - 4:
  • 3×(-5)² + 7×(-5) - 4 = 75 - 35 - 4 = 36.

Fractional Evaluations

• If a=6 and b=-2, evaluate (a-b)/(a+b):
  • (6-(-2))/(6+(-2)) = (6+2)/(6-2) = 8/4 = 2.
• For m=4 and n=3, find (m²-n²)/(m²+n²):
  • (4²-3²)/(4²+3²) = (16-9)/(16+9) = 7/25.
• If x=4 and y=12, evaluate 1/x + 1/y:
  • 1/4 + 1/12 = 3/12 + 1/12 = 4/12 = 1/3.