Algebra Class: Simplifying Expressions and Equations
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Questions and Answers

What is -y + 9z - 16y - 25z + 4 written in simplest form?

  • -29yz
  • 17y + 34z + 4
  • -17y - 16z + 4 (correct)
  • 17y + 16z + 4

    • What is 8z + x - 5 - 9z + 2 written in simplest form?

  • x + z - 3 (correct)
  • x + 17z + 7
  • x - z - 3
  • x - 17z - 3

    • Use the Distributive Property to expand 2(-3x + 5).

    -6x + 10

    Use the Distributive Property to expand -7(x - 2).

    <p>-7x + 14</p> Signup and view all the answers

    Simplify 2x + 5 + x.

    <p>3x + 5</p> Signup and view all the answers

    Simplify -4 + 6n + 2 - 3n.

    <p>3n - 2</p> Signup and view all the answers

    Find (8x + 9) + (-6x - 2).

    <p>2x + 7</p> Signup and view all the answers

    Find (-2x + 10) + (-8x - 1).

    <p>-10x + 9</p> Signup and view all the answers

    Find the additive inverse of 3x - 6.

    <p>-3x + 6</p> Signup and view all the answers

    Find (3x - 4) - (x - 5).

    <p>2x + 1</p> Signup and view all the answers

    Find the GCF of 4y and 12y.

    <p>4y</p> Signup and view all the answers

    Find the GCF of 16mn and 24m.

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

    Factor 5x + 35. If the expression cannot be factored, write cannot be factored.

    <p>5(x + 7)</p> Signup and view all the answers

    Simplify 3(x + 4) + 5x. Write your answer in factored form.

    <p>8x + 12</p> Signup and view all the answers

    Simplify -5(2x - 6) + 25x. Write your answer in factored form.

    <p>15x + 30</p> Signup and view all the answers

    Simplify 2(-8x - 3) + 18x. Write your answer in factored form.

    <p>2x - 6</p> Signup and view all the answers

    Solve 6 + y = -8.

    <p>-14</p> Signup and view all the answers

    Solve -12 = 4 + c.

    <p>-16</p> Signup and view all the answers

    Solve -7x = 56.

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

    Solve 15 = -z/8.

    <p>-120</p> Signup and view all the answers

    Solve -8 = 2/3n.

    <p>-12</p> Signup and view all the answers

    Solve -3x - 9 = -15.

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

    Solve 4(x + 8) = 44.

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

    Solve -5(x - 10) = -35.

    <p>17</p> Signup and view all the answers

    Solve 0.4(x - 7) = 18.

    <p>52</p> Signup and view all the answers

    Flashcards

    Simplifying expressions

    Combining like terms to reduce an expression to its simplest form.

    Distributive Property

    Multiplying each term inside parentheses by a factor outside.

    Additive inverse

    A number that, when added to the original number, results in zero.

    GCF

    Greatest Common Factor; the largest number that divides all terms.

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    Factoring expressions

    Breaking down an expression into products of simpler expressions.

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    Combining like terms

    Adding or subtracting terms that have the same variable.

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    Solving equations

    Finding the value of the variable that makes the equation true.

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    Value of y when y = -8

    Solve the equation 6 + y = -8; y = -14.

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    Value of c when c = -16

    Solve -12 = 4 + c; c = -16.

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    Value of x when x = 3

    Solve 5x + 2 = 17; x = 3.

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    Value of x when x = 4

    Solve 7(x + 8) = 49; x = 4.

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    Value of n when n = -0.32

    Solve -8 = 25n; n = -0.32.

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    Value of b when b = 4

    Solve -20 = -5b; b = 4.

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    Value of x when x = -3

    Solve 0.4(x - 7) = 18; x = 52.5.

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    Value of x when x = 5

    Solve -3x - 9 = -15; x = 5.

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    Sum of (x + z - 3)

    Simplify the expression 8z + x - 5 - 9z + 2 to x + z - 3.

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    Value of z when z = -3

    Solve -12 = 4 + c; c = -16.

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    Expanded form of 2(-3x + 5)

    Using the Distributive Property, it becomes -6x + 10.

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    Combining 8x + 9 + (-6x - 2)

    Simplify to 2x + 7.

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    Factoring 5x + 35

    Factoring gives 5(x + 7) as the simplest product.

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    Value of y when y = -10

    Solve for y in the equation -6x - 7 = 17.

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    Value of m when m = 1

    Solve the equation 19 = 4x + 3 for x; x = 4.

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    Value of x when x = -2

    Solve 4(x + 8) = 44 for x; x = -2.

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    Factor expression 8x - 14

    Becomes 2(4x - 7) after factoring out common term.

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    Value of x when x = 6

    Solve -7(x - 2); x = 6 after simplification.

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    Expression (3x - 4) - (x - 5)

    Simplifies to 2x + 1 after careful distribution and combining.

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    Expression (−3x + 2) + (4x - 5)

    Becomes x - 3 after combining like terms.

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    Study Notes

    Simplifying Expressions

    • Combine like terms to simplify expressions.
    • Combine terms with the same variables and exponents.
    • Example: -y + 9z – 16y – 25z + 4 simplifies to -17y - 16z + 4.
    • Another example: 8z + x − 5 − 9z + 2 simplifies to x − z − 3.

    Distributive Property

    • Distribute a number to each term within parentheses.
    • Example: 2(-3x + 5) expands to -6x + 10.
    • Another example: 6(-4x + 3y) expands to -24x + 18y.

    Combining Expressions

    • Combining terms from different parentheses.
      • Expand parentheses and then simplify.
    • Example: (5x + 4) + (-8x - 2) simplifies to -3x + 2.
    • Example: (-2x + 10) + (-8x - 1) simplifies to -10x + 9

    Additive Inverse

    • Additive inverse of any expression is the opposite sign for each term
    • Example: additive inverse of 3x - 6 is -3x + 6
    • Example: additive inverse of -4x - 8 is 4x + 8

    Solving Equations

    • Isolate the variable to solve for its value.
    • Example: -20 = -5b, solve for b: b = 4
    • Example: 5x + 2 = 17, solve for x: x = 3
    • Example: -18 = 6 + 6x, solve for x: x = -4

    Factoring

    • Factor out common factors from expressions.
    • Example: Factor 5x + 35. Answer is 5(x +7).

    Solving Multi-Step Equations

    • Use multiple steps to isolate the variable, combining like terms and performing opposite operations and distributive properties
    • Example: Solve -7x - 4 = 12 by adding 4, dividing by -7 -7x = 16 x = -16/7

    Finding the Greatest Common Factor (GCF)

    • Find the highest factor common to multiple terms.
    • Example: Find GCF of 4y and 12y. Answer is 4y

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    Description

    Test your knowledge on simplifying expressions, using the distributive property, and solving equations. This quiz covers combining like terms, applying additive inverses, and isolating variables. Challenge yourself to reinforce your algebra skills.

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