Lesson 3.3.1

HW: 3-81 to 3-86

Learning Target: Scholars will solve linear equations that involve multiplication. Scholars will solve problems that involve absolute value.

Now that you know how to multiply algebraic expressions, you can solve equations that involve multiplication. You will also solve equations that have an absolute value in them.

3-76. Review what you learned in Lesson 3.2.4 by multiplying each expression below. First decide if you will multiply each expression using the Distributive Property or using a generic rectangle. Remember to simplify your result.

  1. (6x − 11)(2x + 5)
  2. −2x2(15x2 − 3t)
  3. (6 − y)(y + 2)
  4. 16(3 − m2)

3-77.Work with your team to solve each of these equations. Use the Distributive Property or draw generic rectangles to help you rewrite the products. Be sure to record your algebra work for each step.

  1. 2(y −2) = −6
  2. 5x2+ 43 = (x− 1)(5x + 6)
  3. (x+ 3)(x+ 4) =(x+ 1)(x+ 2)
  4. 2(x+ 1) + 3 = 3(x− 1)

3-78.ABSOLUTE VALUE EQUATIONS

Find as many solutions to the following equations as you can.

  1. = 5
  2. = 133
  3. = −2

3-79.Solve. Work with your team to organize your work so that anyone could follow along to find both solutions.

3-80. Solve.Record your steps.

3-81.Find each of the following products by drawing and labeling a generic rectangle or by using the Distributive Property.

  1. −4y(5x + 8y)
  2. 9x(− 4+ 10y)
  3. (x2 − 2)(x2 + 3x + 5)

3-82.Is the set of even numbers closed under addition? That is, if you add two even numbers, do you always get an even number? Is the set of odd numbers closed under addition? Explain your answers.

3-83. Find the dimensions of the generis rectangle at right. Then write an equivalency statement (length · width = area) of the area as a product and as a sum.

3-84. Solve forx. Use any method. Check your solutions by testing them in the original equation.

3-85.Copy and complete each of the Diamond Problems below. The pattern used in the Diamond Problems is shown at right.

3-86.Iff(x) =7 +andg(x) =x3− 5, then find:

  1. f(−5)
  2. g(4)
  3. f(0)
  4. f(2)
  5. g(−2)
  6. g(0)

Lesson 3.3.1

  • 3-76. See below:
  • 12x2+ 8x − 55
  • −30x4+ 6x2t
  • −y2+ 4y + 12
  • 48 − 16m2
  • 3-77. See below:
  • y = −1
  • x = 49
  • x = −2.5
  • x = 8
  • 3-78. See below:
  • x = −5 or 5
  • x = −133 or 133
  • no solution
  • x = −3 or 17
  • 3-79.x = 7 or −
  • 3-80.x= 1 or
  • 3-81. See below:
  • −20xy − 32y2
  • −36x + 90xy
  • x4 + 3x3 + 3x2− 6x− 10
  • 3-82. Yes, for even numbers. On a number line, if you start at any multiple of two and add a multiple of two (an even number), you will always be stepping up the number line in multiples of two; you will always land on an even number. No for odd numbers. For example, 3 + 5 = 8; the sum of two odd numbers is not always odd.
  • 3-83. (x − 5)(x + 3) = x2 − 2x− 15
  • 3-84. See below:
  • x = 8x = −2
  • x= ±7
  • x = 1x= −3
  • no solution
  • 3-85.Find solutions in the diamonds below:
  • 3-86. See below:
  • 12
  • 59
  • 7
  • 9
  • −13
  • −5