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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