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Bell Ringer

Bell Ringer. Darius spent $4 more than twice what Kyla spent. If Kyla spent “k” dollars, write an expression for the amount of money Darius spent. If Darius spent $24, how much did Kyla spend? (Now its an equation!) 2k + 4 = 24. + 4. 2k. $4 more than twice Kyla. Twice Kyla.

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Bell Ringer

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  1. Bell Ringer • Darius spent $4 more than twice what Kyla spent. If Kyla spent “k” dollars, write an expression for the amount of money Darius spent. • If Darius spent $24, how much did Kyla spend? (Now its an equation!) 2k + 4 = 24 + 4 2k $4 more than twice Kyla Twice Kyla

  2. XEI 202: Solve equations in the form x + a = b, where a and b are whole numbers or decimals XEI 302: Solve one-step equations having integer or decimal answers XEI 403: Solve routine first-degree equations Solving One-Step Equations with Addition and Subtraction

  3. Equations • An equation is a sentence that states that two mathematical expressions are equal. Example: x + 3 = 7 What would be the value of the “?” to balance the scale! The “?” represents “x”, an unknown value. ? The goal is to find the value of “x” to balance the scale!

  4. Solving One-Variable Equations 1. Isolate the variable by applying the opposite operation to each side. • First, use the opposite operation of addition or subtraction. • Second, use the opposite operation of multiplication or division. 2. Check your answer.

  5. The Golden Rule The Golden Rule of Algebra: “What you do to one side, you must do to the other!”

  6. Example: #1 x + 5 = 9 – 5 – 5 In order to isolate the “x”, we must get rid of the + 5, so we perform the opposite operation, - 5. x = 4 We are left with “x” on one side and 4 on the other, thus x = 4! Check: x + 5 = 9 4 + 5 = 9 Yes, it checks out! The red line separates the two sides of the equation!

  7. Example: #2 x – 3 = 7 Golden Rule: If we add 3 to one side, we add 3 to the other! + 3 + 3 x = 10 Check: 10 – 3 = 7 Yes!!!! – 3 + 3 = 0, so we are left with “x”!

  8. Example: #3 6 + x = 3 The 6 is assumed to be positive if it has no sign. – 6 – 6 x = -3 Check: 6 + -3 = 3 Yes!!!!

  9. Example: #4 8 – x = 7 When we subtract the 8, we are left with a –x! – 8 – 8 –x = –1 x = 1 Change the sign of each side! Check: 8 – 1 = 7 Yes!!!!

  10. Your Turn – Add & Subtract • x = 20 • x = 8 • x = 14 • x = -5 • x = 13 • x = 11 • x = -7.5 • x = -8.2 • x – 5 = 15 • 6 + x = 14 • x – 9 = 5 • 5 – x = 10 • -5 + x = 8 • -x + 4 = -7 • -2.5 – x = 5 • x + 1.2 = -7

  11. XEI 202: Solve equations in the form x + a = b, where a and b are whole numbers or decimals XEI 302: Solve one-step equations having integer or decimal answers XEI 403: Solve routine first-degree equations Solving One-Step Equationswith Multiplication and Division

  12. Multiplication and Division Now we have solved equations involving addition and subtraction, we will move to multiplication and division. The “Golden Rule of Algebra” still applies! "What you do to one side of the equation, you must do to the other!”

  13. Example: #1 In order to isolate “x”, we must get rid of the 3!!! 3x = 9 9/3 = 3, so x = 3! 3 3 x = 3 Golden Rule: If we divide one side by 3, we must divide the other side by 3! Check: 3 • 3 = 9 Yes!!!!

  14. Example: #2 In order to isolate “x”, we must get rid of the -4!!! -4x = 20 20/-4 = -5, so x = -5! -4 -4 x = -5 We divide both sides by -4!!! Check: -4 • -5 = 20 Yes!!!!

  15. Example: #3 1 x = 5 4 4 1 4 Multiply by the reciprocal! . Follow Golden Rule! . x = 5 4 1 1 5•4 x = 1 x = 20

  16. Example: #4 Reciprocal Do the same!

  17. Your Turn – Multiply & Divide • x = 7 • x = -5 • x = • x = • x = 16 • x = 15 • x = 12 • x = • 5x = 35 • -3x = 15 • 2x = 7 • -6x = 20 • ½ x = 8 • 2/5 x = 6 • ¼ x = 3 • 2/3 x = 7

  18. Tomorrow… • Perform word to symbol translation and solving one-step, one-variable equations. • In other words…solve word problems!!!!

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