Lesson 3.3.3

HW: 3-107 to 3-112

Learning Target: Scholars will solve single- and multi-variable linear equations.

You have been developing your equation-solving skills in this chapter. Today you will practice solving several types of equations. At the end of the lesson, you will summarize everything you know about solving equations.

3-105.Your teacher will explain the way you will work today on the problems below. Asyou work, be sure to record all of your steps carefully. Check your solutions, if possible.

  1. Solve for c: E = mc2
  2. Solve form:
  3. Solve forx: −6 = −6(3x −8)
  4. Solve fory: 3x + 6y = 24
  5. Solve forx: 2−3(2x −1) = 17
  6. Solve fory:
  7. Solve forx: y = −3x + 4
  8. Solve forx: x(2x −1) = 2x2 + 5x −12
  9. Solve forw: 2(v−3) = 1 − (w + 4)
  10. Solve forx: 4x(x+ 1) = (2x −3)(2x + 5)

3-107.Solve each equation.

  1. 3(x −2) = −6
  2. 2(x+1) + 3 =3(x−1)
  3. (x + 2) (x + 3) =(x + 1) (x + 5)

3-108.Find the equation of the line based on the table. 3-108 HW eTool (Desmos).

x / 3 / −2 / 5 / 12
y / 4 / −11 / 10 / 31

3-109. Find an equation of the line with slope passing through the point (10, 9). 3-109 HW eTool (Desmos).

3-110.This problem is a checkpoint for operations with rational numbers. It will be referred to as Checkpoint 3.

Compute each of the following problems with fractions.

Check your answers by referring to the Checkpoint 3 materials.

Ideally, at this point you are comfortable working with these types of problems and can solve them correctly. If you feel that youneed more confidence when solving these types of problems, then review theCheckpoint 3 materials and try the practice problems provided. From this point on, you will be expected to do problems like these correctly and with confidence.

3-111. Copy and complete these generic rectangles on your paper. Then write the area of each rectangle as a product of the length and width and as a sum of the parts.

3-112.Simplify using only positive exponents.

  1. (3x2y)(5x)
  2. (x2y3)(x−2y−2)
  3. (2x−1)3

Lesson 3.3.3

  • 3-105. See below:
  • x = 3
  • y = −x + 4
  • x = −2
  • y = 0 or y =
  • x = 2
  • w = 3 − 2y
  • no solution
  • 3-107. See below:
  • x = 0
  • x = 8
  • x = 1
  • x = −3, 13
  • 3-108.y = 3x − 5
  • 3-109.y = x + 7
  • 3-110. See below:
  • 4
  • = 1
  • − = −2
  • −3
  • 2
  • 3-111. See below:
  • 6(13x − 21) = 78x − 126
  • (x + 3)(x − 5) = x2 − 2x − 15
  • 4(4x2 − 6x+ 1) = 16x2 −24x + 4
  • (3x − 2)(x + 4) = 3x2 + 10x − 8
  • 3-112. See below:
  • 15x3y
  • y
  • x5