Math Journal 10-16 −3𝑥+𝑦=7 2. 10𝑥 −5𝑦=25 Rearrange the equation so that y is a function of x −3𝑥+𝑦=7 2. 10𝑥 −5𝑦=25 Solve for x. 3. − 𝑥−1 +5𝑥=5𝑥+17 4. −2𝑥−5≥11

Math Journal 10-15 𝑚= 1 3 𝑛𝑡 𝑓𝑜𝑟 𝑛 2. 9 5 𝐶+32=𝐹 𝑓𝑜𝑟 𝐶 Solve the formula for the given variable. 𝑚= 1 3 𝑛𝑡 𝑓𝑜𝑟 𝑛 2. 9 5 𝐶+32=𝐹 𝑓𝑜𝑟 𝐶 Solve for x. 3. −2 𝑥−3 +4𝑥=5𝑥−12 4. 3𝑥−8≥13

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?

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

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

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

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

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

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

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

.36 + .03x > .06x - .03x - .03x .36 > .03x .03 .03 12 > x 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 .36 > .03x .03 .03 12 > x x < 12

Justin will weigh less than Tyson up until the 15 week mark. 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? Justin Tyson 150 + 2x < 195 - 1x + 1x + 1x Justin will weigh less than Tyson up until the 15 week mark. 150 + 3x < 195 - 150 - 150 3x < 45 3 3 x < 15

Summary 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.