Basic Algebra Substitution Flashcards
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Questions and Answers

What does substitution mean in Algebra?

Putting numbers where the letters are.

If x = 6, what is the value of x - 2?

4

When x = 2, what is the value of 10/x + 4?

9

When x = 5, what is the value of x + x/2?

<p>7.5</p> Signup and view all the answers

If x = 3 and y = 4, what is the value of x² + xy?

<p>21</p> Signup and view all the answers

If x = 3 (unknown y), what is the value of x² + xy?

<p>9 + 3y</p> Signup and view all the answers

If x = -2, what is the value of 1 - x + x²?

<p>7</p> Signup and view all the answers

If x = 4, what is the value of 12/x + 3?

<p>6</p> Signup and view all the answers

If y = 10, what is the value of 5(y - 4)/2?

<p>15</p> Signup and view all the answers

If x = 2 and y = 3, what is the value of xy + y²?

<p>15</p> Signup and view all the answers

If x = 5 and y = 6, what is the value of 2x - 12/y?

<p>8</p> Signup and view all the answers

If x = 4 and y = 2, what is the value of x² + y³?

<p>24</p> Signup and view all the answers

If z = -3, what is the value of z² - z - 1?

<p>11</p> Signup and view all the answers

If y = -5, what is the value of 3y² + 7y - 4?

<p>36</p> Signup and view all the answers

If a = 6 and b = -2, what is (a - b) / (a + b)?

<p>2</p> Signup and view all the answers

If m = 4 and n = 3, what is (m² - n²) / (m² + n²)?

<p>7/25</p> Signup and view all the answers

If x = 4 and y = 12, what is 1/x + 1/y?

<p>1/3</p> Signup and view all the answers

Study Notes

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.

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Test your knowledge on substitution in algebra with these flashcards. Learn how to replace variables with specific numbers and solve equations easily. Perfect for beginners looking to strengthen their algebra skills.

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