Algebra I 1.4 Write Equations And Inequalities. VOCAB Equation – a mathematical sentence formed by placing the symbol = between two expressions Inequality.

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Algebra I 1.4 Write Equations And Inequalities

VOCAB Equation – a mathematical sentence formed by placing the symbol = between two expressions Inequality – a mathematical sentence formed by placing one of the symbols, ≤, or ≥ between two expressions

VOCAB Open Sentence – an equation or inequality that contains an algebraic expression Solution to an Equation –a number that makes the sentence true Solution to an Inequality – a number or set of numbers that makes the sentence true

1.4 Write Equations and Inequalities SymbolMeaningAssociated Words =is equal toThe same as <is less thanFewer than >is greater thanMore than ≤is less than or equal toAt most; no more than ≥is greater than or equal toAt least; no less than

1.4 Write Equations and Inequalities The BIG Difference The BIG Difference Equations: Equations: Have ONLY ONE Solution! Have ONLY ONE Solution! Inequalities: Inequalities: Have MANY Solutions!!!!! Have MANY Solutions!!!!!

Write equations and inequalities EXAMPLE 1 a. The difference of twice a number k and 8 is 12. b. The product of 6 and a number n is at least 24. 6n ≥ 24 Verbal SentenceEquation or Inequality 2k – 8 = 12

GUIDED PRACTICE for Example 1 d. Write an equation or an inequality: The quotient of a number p and 12 is at least 30. ANSWER P 12 > – 30 c. A number y is no less than 5 and no more than ≤ y ≤ 13

Check possible solutions EXAMPLE 2 Check whether 3 is a solution of the equation or inequality. a. 8 – 2x = 2 c. 2z + 5 > 12 b. 4 x – 5 = 6 d n ≤ 20 4(3) – 5 6 ? = 8 – 2(3) 2 ? = 2(3) > ? 5 + 3(3) 20 ≤ ? Equation/Inequality Substitute Conclusion 2 = 2 3 is a solution.  14 ≤ 20 3 is a solution.  7 = 6 3 is not a solution. X 11 > 12 3 is not a solution. X

GUIDED PRACTICE for Example 2 Check to see whether or not 5 is a solution of the equation or inequality. a. 9 – x = 4 b. b + 5 < 15 9 – 5 4 ? = Equation/Inequality Substitute Conclusion 4 = 4 5 is a solution.  < ? 10<15 5 is a solution.  c. 2n > – is NOT a solution. > – 2(5) > – ? X

EXAMPLE 3 Use mental math to solve an equation Equation a. x + 4 = 10 b. 20 – y = 8 c. 6n = 42 a 5 =9 d.d. Think What number plus 4 equals 10? 20 minus what number equals 8? 6 times what number equals 42? What number divided by 5 equals 9? Solution Check 20 –12 = 8  = 10  6(7) = 42  =9  45

GUIDED PRACTICE for Example 3 Solve the equation using mental math. Equation 5. m + 6= x = 40 Think What number plus 6 equals 11? 5 times what number equals 40? What number divided by 4 equals 10 Solution Check 5(8) = 40  = 11  40 = 10  4 7. r = 10 4

Is 2 a solution to 4z – 5 < 3? Answer Now 1. A solution 2. NOT a solution

Solve for f: Answer Now

Solve a multi-step problem EXAMPLE 4 The last time you and 3 friends went to a mountain bike park, you had a coupon for $10 off and paid $17 for 4 tickets. What is the regular price of 4 tickets ? If you pay the regular price this time and share it equally, how much does each person pay ? Mountain Biking

Solve a multi-step problem EXAMPLE 4 Step 1: Write a verbal model. Let p be the regular price of 4 tickets. Write an equation. Regular Price – Coupon = Amount Paid P – 10 = 17

Solve a multi-step problem EXAMPLE 4 Step 2: Use mental math to solve the equation p – 10 = 17. Think: 10 less than what number is 17? Because 27 – 10 = 17, the solution is 27. Answer: The regular price for 4 tickets is $27. Step 3: Find Cost Per Person $27 / 4 people = 6.75 Answer: $6.75 per person.

GUIDED PRACTICE for Examples 4 and 5 WHAT IF? Suppose that the price of 4 tickets with a half-off coupon is $15. What is each person’s share if you pay full price?

GUIDED PRACTICE for Examples 4 and 5 STEP 1: Write a verbal model. Let p be the regular price of 4 tickets. Write an equation. Regular Price – Coupon = Amount Paid r – 15 = 15

GUIDED PRACTICE for Examples 4 and 5 STEP 2: Use mental math to solve the equation p – 15=15. Think: 15 less than what number is 15? Because 30 – 15 = 15, the solution is 30. So the full price is $30. STEP 3: Find the Cost Per Person $30/4 = 7.5 Answer: $7.50 per person

Write and check a solution of an inequality EXAMPLE 5 STEP 1: Write a verbal model. Let p be the average number of points per game. Write an inequality. Number of Games Number of Points Per Game > Total Points Last Year 18 p > 351 STEP 2: Check that 20 is a solution of the in equality18p > (20) = > 351 Answer: An average of 20 points per game will be enough.

GUIDED PRACTICE for Examples 4 and 5 WHAT IF Suppose that the player plays 16 games. Would an average of 22 points per game be enough to beat last year’s total? STEP 1: Write a verbal model. Let p be the average number of points per game. Write an inequality. Number of Games Number of Points Per Game = Total Points Last Year STEP 2: Check that 22 is a solution of the in equality16p > 351. Because 16(22) = > 351 So, 22 is a solution.