Warm-Up 1. 𝒙 𝟑 +𝟐 𝒘𝒉𝒆𝒏 𝒙=𝟏𝟐 True or false? 2. 𝟐𝒙+𝟑 𝒆𝒒𝒖𝒂𝒍𝒔 𝟗 𝒘𝒉𝒆𝒏 𝒙=𝟑 3. 𝟓𝒙 𝒆𝒒𝒖𝒂𝒍𝒔 𝟏𝟓 𝒘𝒉𝒆𝒏 𝒙=𝟐 4. It is estimated that the earth weighs 6 sextillion tons. How much more would the earth weigh if one sextillion tons of concrete and stone were used to build a large wall?

Warm-Up 6 1. 𝒙 𝟑 +𝟐 𝒘𝒉𝒆𝒏 𝒙=𝟏𝟐 True or false? 2. 𝟐𝒙+𝟑 𝒆𝒒𝒖𝒂𝒍𝒔 𝟗 𝒘𝒉𝒆𝒏 𝒙=𝟑 𝑻𝒓𝒖𝒆 3. 𝟓𝒙 𝒆𝒒𝒖𝒂𝒍𝒔 𝟏𝟓 𝒘𝒉𝒆𝒏 𝒙=𝟐 𝑭𝒂𝒍𝒔𝒆

4. It is estimated that the earth weighs 6 sextillion tons 4. It is estimated that the earth weighs 6 sextillion tons. How much more would the earth weigh if one sextillion tons of concrete and stone were used to build a large wall? The same, since all materials are taken from the earth’s original weight.

1.4 Equations and Inequalities Objective: Be able to identify inequalities and equations. Solve simple equations and inequality problems involving a variable.

Your must bring at least $8.70 with you. You want to go to IN-N-OUT burger for dinner. You want to buy a double-double for $3.25, a soda for $1.95 and an animal style fries for $3.50. At least how much money do you need to bring with you? 𝟑.𝟐𝟓 𝟏.𝟗𝟓 𝟑.𝟓𝟎 𝟖.𝟕𝟎 Your must bring at least $8.70 with you.

1.4 Equations and Inequalities 1. What is an Expression? This is like part of a sentence: 𝟐𝒙−𝟏 2. What is an equation? Equations are formed when an equal sign is placed between two expressions. 𝟐𝒙−𝟏=𝟕 2. What is an Inequality? These are like equations except instead of using =, 𝒊𝒏𝒆𝒒𝒖𝒂𝒍𝒊𝒕𝒊𝒆𝒔 𝒖𝒔𝒆 <,>,≤,≥,≠ 𝟐𝒙−𝟏≥𝟕

1.4 Equations and Inequalities 𝟐𝒙+𝟑 𝒆𝒒𝒖𝒂𝒍𝒔 𝟗 𝒘𝒉𝒆𝒏 𝒙=𝟑 𝟐(𝟑)+𝟑=𝟗 𝟔+𝟑=𝟗 𝒀𝒆𝒔

1.4 Equations and Inequalities 𝑾𝒉𝒂𝒕 𝒅𝒐𝒆𝒔 𝒕𝒉𝒊𝒔 𝒎𝒆𝒂𝒏? 𝒙>𝟔 -1 1 2 3 4 5 6 7 𝒙≤−𝟑 -4 -3 -2 -1 1 2 3 4

1.4 Equations and Inequalities 1. 𝟖𝒙+𝒙≥𝟏𝟖 𝒘𝒉𝒆𝒏 𝒙=𝟐 𝟖 𝟐 +𝟐≥𝟏𝟖 𝒀𝒆𝒔 𝟏𝟔+𝟐≥𝟏𝟖 𝟏𝟖≥𝟏𝟖 2. 𝟔𝒗−𝟏≥𝟏𝟕 𝒘𝒉𝒆𝒏 𝒗=𝟑 𝟔 𝟑 −𝟏≥𝟏𝟕 𝒀𝒆𝒔 𝟏𝟖−𝟏≥𝟏𝟕 𝟏𝟕≥𝟏𝟕

1.4 Equations and Inequalities 1. 𝟖𝒙+𝒙≥𝟏𝟖 𝒘𝒉𝒆𝒏 𝒙=𝟐 𝟖 𝟐 +𝟐≥𝟏𝟖 𝒀𝒆𝒔 𝟏𝟔+𝟐≥𝟏𝟖 𝟏𝟖≥𝟏𝟖 2. 𝟔𝒗−𝟏≥𝟏𝟕 𝒘𝒉𝒆𝒏 𝒗=𝟑 𝟔 𝟑 −𝟏≥𝟏𝟕 𝒀𝒆𝒔 𝟏𝟖−𝟏≥𝟏𝟕 𝟏𝟕≥𝟏𝟕

1.4 Equations and Inequalities 𝟏. 𝒃 𝟕 +𝟑>𝟏𝟐 𝒘𝒉𝒆𝒏 𝒃=𝟐𝟏 (𝟐𝟏) 𝟕 +𝟑>𝟏𝟐 𝑵𝑶 𝟑+𝟑>𝟏𝟐 𝟔>𝟏𝟐 2. 𝒎 𝟐 +𝟖≤𝟕𝟐 𝒘𝒉𝒆𝒏 𝒎=−𝟖 (−𝟖) 𝟐 +𝟖≤𝟕𝟐 𝒀𝒆𝒔 𝟔𝟒+𝟖≤𝟕𝟐 𝟕𝟐≤𝟕𝟐

Yes. I have enough money for 4.16667 tanks of gas. You are taking a trip in your new Prius. You have $125 to help pay for gas. It costs $30 to fill the tank. Can you completely fill the gas tank four times? Use the inequality 𝟑𝟎𝒚≤𝟏𝟐𝟓 to model the situation. What do 30, 𝐲, 𝒂𝒏𝒅 𝟏𝟐𝟓 𝒓𝒆𝒑𝒓𝒆𝒔𝒆𝒏𝒕? Yes. I have enough money for 4.16667 tanks of gas. 30 is the amount need to fill the tank 𝒚 is the number of tanks I have money for 125 is the total amount I have to spend on gas.

What is the difference between the two? Conclusion What is an equation? What is an inequality? What is the difference between the two?

When can we use Equations or Inequalities in real life?

1.4 Equations and Inequalities Equations have equal signs. Solutions make them true. *Is 8 a solution to 3𝑥−1=24? 3 8 −1=24 24−1=24 23≠24 NO 2. Inequalities use <, >, ≤, ≥, ≠ *Is 8 a solution to 3𝑥−1≤24? 3 8 −1≤24 24−1≤24 23≤24 Yes

1.4 Equations and Inequalities 3. Real Life Applications: *Adults weighing 150 pounds should consume no more than 2000 calories a day. One man eats an average of C calories 3 times per day. Find the possible values of C that would keep his calories within proper range. # times eat ∙ calories ≤ proper range 3c ≤ 2000 3 3 c ≤666.6