Review

Solve # A=lw for w v + 6 = 4v – (2x – 4) = 4x + 4

Answers

Let’s try some more equations Remember, we have to keep the equations balanced! Solve each: 8m – 10 = 36 8m – = m = 46 8 m =m = w = 84

Solve. 4x + 6 = x – 4x 6 = –3x To collect the variable terms on one side, subtract 4x from both sides. Since x is multiplied by -3, divide both sides by –3. –2 = x 6 –3 –3x –3 =

Solve. 9b – 6 = 5b + 18 – 5b 4b – 6 = 18 4b4b = To collect the variable terms on one side, subtract 5b from both sides. Since b is multiplied by 4, divide both sides by 4. b = b = 24 Since 6 is subtracted from 4b, add 6 to both sides.

Solve. 1. 4x + 16 = 2x 2. 8x – 3 = x 3. 2(3x + 11) = 6x x = x – 9 5. An apple has about 30 calories more than an orange. Five oranges have about as many calories as 3 apples. How many calories are in each? x = 6 x = –8 no solution x = An orange has 45 calories. An apple has 75 calories.

Solve. 9w + 3 = 9w ≠ 7 9w + 3 = 9w + 7 – 9w To collect the variable terms on one side, subtract 9w from both sides. There is no solution. There is no number that can be substituted for the variable w to make the equation true.

5x  2 = x + 4 Solve each: 5x  = x Notice that there are variables on both sides 5x = x + 6 Get rid of the -2 on the left side Simplify 5x – x = x – x + 6 Get rid of the x on the right side 4x = 6 Get rid of the cofficient of x 4 x = Simplify

Exploration Determine the solution for each equation. 4,4 4, -4 9,9 9, -9 No Solution

Examples Solving basic absolute value equations

Examples continued -24, 8 1, 5

More Examples Solving absolute value equations when there are terms outside the symbols

Even More Examples -2, 6 0, 8/3

6|5x + 2| = 312 Isolate the absolute value expression by dividing by 6. 6|5x + 2| = 312 |5x + 2| = 52 Set up two equations to solve. 5x + 2 = 525x + 2 = -52 5x = 50 5x = -54 x = 10orx = -54/5 Check: 6|5x + 2| = 312 6|5x + 2| = 312 6|5(10)+2| = 312 6|5(-10.8)+ 2| = 312 6|52| = 312 6|-52| = = = 312

3|x + 2| -7 = 14 Isolate the absolute value expression by adding 7 and dividing by 3. 3|x + 2| -7 = 14 3|x + 2| = 21 |x + 2| = 7 Set up two equations to solve. x + 2 = 7 x + 2 = -7 x = 5 or x = -9 Check: 3|x + 2| - 7 = 14 3|x + 2| -7 = 14 3|5 + 2| - 7 = 14 3|-9+ 2| -7 = 14 3|7| - 7 = 14 3|-7| -7 = = = = = 14

In the equation below, what value of “k” would give me a solution of 8 for “w”??? We need to find a value for k that when we solved the equation it would give us a solution of 8 for w. Let’s just plug in 8 for w, and solve for k: Now let’s check to see if 3 works:

5 is subtracted from a number multiplied by 4. That result is equal the same number multiplied by eight then increased by 7. What is the number? First translate this into an equation: Now solve it: The number is -3 -4x -7 4

The difference of two integers is 8. The lesser integer is 34. What is the greater integer? First translate this into an equation: “y” has to be the lesser of the two integers, because if it were larger then you would have a negative value on the right!!! Now solve:

One fifth of a number is twenty- five. What is the number? Now solve:

A baseball hat printing company charges $0.05 per hat plus $5. Another company charges $0.10 per hat. How many hats are in an order that costs the same regardless of which company is used? Company #1: Company #2: x = number of hats ordered If we want to know how many hats are ordered from each company the costs the same, then we will set each equation equal to each other and solve: -0.05x 0.05 So, 100 hats ordered costs the same from either company.

A printer holds 120 sheets of paper. After printing is done it held 54 sheets of paper. Write an equation than can be used to find how many sheets were printed?