Chapter 3 – Solving Linear Equations Algebra I A - Meeting 14 Homework # 10 – Word Problems pg 152 # 40 To qualify for a lifeguard training course, you.

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Chapter 3 – Solving Linear Equations Algebra I A - Meeting 14 Homework # 10 – Word Problems pg 152 # 40 To qualify for a lifeguard training course, you have to swim continuously for 500 yards using either the front crawl or the breaststroke. You swim the front crawl at a rate of 45 yards per minute and the breaststroke at a rate of 35 yards per minute. You take 12 minutes to swim the 500 yards. How much time did you spend swimming the front crawl?

Chapter 3 – Solving Linear Equations Algebra I A - Meeting 14 Section 3.4 – Solve Equations with Variables on Both Sides Example # 1 Solve for x : Write the original equation. Simplify Check your Solution. Isolate the Variable, Subtract 2x from each side Divide each side by 3. Isolate the Variable, Subtract 13 from each side Simplify

Chapter 3 – Solving Linear Equations Algebra I A - Meeting 14 Example # 2 Solve for x : Write the original equation. Simplify Check your Solution. Isolate the Variable, Add 5 to each side Divide each side by 3. Distribute 1/5 into (5x +20) Section 3.4 – Solve Equations with Variables on Both Sides Isolate the Variable, Subtract x from each side Simplify

Chapter 3 – Solving Linear Equations Algebra I A - Meeting 14 Section 3.4 – Solve Equations with Variables on Both Sides Guided Practice pg 155 # 1 -6 Work in Pairs or Individually

Chapter 3 – Solving Linear Equations Algebra I A - Meeting 14 Currently, you have $80 and your sister has $145. You decide to save $6 of your allowance each week, while your sister decides to spend her whole allowance plus $7 each week. How long will it be before you have as much money as your sister? Add 7x to each side Your Total Savings + (dollars) Your Sister’s Allowance Spent (dollars per week) Your Sister’s Total Savings - (dollars) Simplify Write Equation (x) = 145 – 7(x) Subtract 80 from each side Write a verbal model. Let x be the Total # of weeks 80 +6x +7x = x +7x x = x = It will take 5 weeks for you and your sister to have the same amount of savings. Example # 3 Your Allowance Saved (dollars per week) Total * # of Weeks = (weeks) Total * # of Weeks (weeks) Simplify Divide 13 from each side 13x = 65 13x/13 = 65/13 Simplify x = 5 Section 3.4 – Solve Equations with Variables on Both Sides

Chapter 3 – Solving Linear Equations Algebra I A - Meeting 14 Example # 4 Solve the equation. If possible : Original equation. Subtract 5x from each side Simplify Distributive Property a) The equation has no solution, because the statement -6 = -5 is not true. Original equation. Subtract 5x from each side Simplify Distributive Property b) The statement 6x+8 = 6x+8 is true for all values of x. So, the equation is an identity, and the solution is all real numbers. Section 3.4 – Solve Equations with Variables on Both Sides

Chapter 3 – Solving Linear Equations Algebra I A - Meeting 14 Steps for Solving Linear Equations Step 1 : Use the distributive property to remove any grouping symbols. Section 3.4 – Solve Equations with Variables on Both Sides Step 2 : Simplify the expression on each side of the equation. Step 3 : Use properties of equality to collect the variable terms on one side of the equation and the constant terms on the other side of the equation. Step 4 : Use properties of equality to solve for the variable. Step 5 : Check your solution in the original equation.

Chapter 3 – Solving Linear Equations Algebra I A - Meeting 14 Homework # 11 pg # 5 – 50 mults. of 5; # 27, # 28 Section 3.4 Study for Quiz on Section 3.1 – 3.4