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Math Journal 10-16

Math Journal 10-16. Rearrange the equation so that y is a function of x 2. Solve for x. 3. 4. Math Journal 10-15. Solve the formula for the given variable. 2. Solve for x. 3. 4. Unit 3 Day 7: Solving Inequalities with Variables on Both Sides.

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Math Journal 10-16

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  1. Math Journal 10-16 Rearrange the equation so that y is a function of x • 2. • Solve for x. • 3. 4.

  2. Math Journal 10-15 Solve the formula for the given variable. • 2. • Solve for x. • 3. 4.

  3. Unit 3 Day 7: Solving Inequalities with Variables on Both Sides • Essential Questions: How do we solve inequalities with variables on both sides? When does an inequality have no solution or a solution of all real numbers?

  4. Vocabulary • No solution: when the variable in an equation or inequality is eliminated and you are left with a false statement • All real numbers: when the variable in an equation or inequality is eliminated and you are left with a true statement

  5. x • x • < 1 • > 4 • 9 • 9 • 9 • 9 • 9x • 9x • > 36 • < 9 • Example 1: Solve the inequalities. • 7x + 19 > -2x + 55 6x + 22 < -3x + 31 • 9x • 9x • + 19 • + 22 • > 55 • < 31 • + 2x • + 2x • + 3x • + 3x • - 19 • -19 • - 22 • -22

  6. -2 • 1 • -2 • 2 • -12 • -12 • Example 2: Solve the inequalities. • x + 2 > 3x + 1 -8x + 7 < 4x – 5 • -12x • < -12 • -2x • > -1 • x < • -2x + 2 • > 1 • -12x + 7 • < - 5 • - 3x • - 3x • - 4x • - 4x • - 7 • - 7 • - 2 • - 2 • x > 1

  7. -3x • + 4 • -6 • -6 • 4 • -6x • < 12 • 1 • -6x + 4 • < 16 • Example 3: Solve the inequality. • (-12x + 16) < 10 – 3(-x – 2) • -3x • + 4 • + 3x • + 6 • < 10 • < 16 • + 3x • - 3x • - 3x • - 4 • - 4 • x > -2

  8. 16x • < 16 • 2 • 16 • 16 • Example 4: Solve the inequality. • (12x – 4) < 2(7 – 5x) • 1 • 16x • - 2 • < 14 • 6x • - 2 • < 14 • - 10x • + 10x • + 10x • + 2 • + 2 • x < 1

  9. 3 • 3 • - x • + 3 • > 3 • Example 5: Solve the inequalities. • 12 – 2a < - 5a – 9 x – 2x + 3 > 3 – x • 3a • < - 21 • > 3 • 3 • 12 • + 3a • < - 9 • + 5a • + 5a • - x • + x • + x • - 12 • - 12 • true statement • infinite solutions • a < -7

  10. > 5y • - 4 • + 6 • -2y • 5x • > -10 • < -25 • - 4 • + 24 • > 5y • 24 • -2 • -2 • Example 6: Solve the inequalities. • 5x + 24 < 5(x - 5) 6y - (3y - 6) > 5y - 4 • -2y + 6 • > • - 4 • < 5x • - 25 • + 6 • 6y • - 3y • - 5x • - 5x • 3y • - 5y • - 5y • false statement • no solutions • - 6 • - 6 • y < 5

  11. .03 • .03 • .36 > .03x • Example 7: Phone Company A charges an activation fee of 36 cents and then 3 cents per minute. Phone Company B charges 6 cents per minute with no activation fee. For what value of x is Phone Company A more expensive than Phone Company B? • .36 + .03x > .06x • Phone Company A is more expensive when the number of minutes is less than 12. If you talk for more than 12 minutes, Phone Company A is a good choice. • - .03x • - .03x • 12 > x • x < 12

  12. 3 • 3 • 150 + 3x < 195 • Example 8: Justin and Tyson are beginning an exercise program to train for football season. Justin weighs 150 pounds and hopes to gain 2 pounds per week. Tyson weighs 195 pounds and hopes to lose 1 pound per week. If the plan works, for how many weeks will Justin weigh less than Tyson? • 3x < 45 • Justin • Tyson • < 195 - 1x • 150 + 2x • + 1x • + 1x • Justin will weigh less than Tyson up until the 15 week mark. • - 150 • - 150 • x < 15

  13. Essential Questions:How do we solve inequalities with variables on both sides? When does an inequality have no solution or a solution of all real numbers? • Take 1 minute to write 2 sentences answering the essential question. Summary

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