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# Module 3, topic 3 notes

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### Module 3, topic 3 notes

1. 1. Module 3, Topic 3 Notes Solving Literal Equations
2. 2. Solving Literal Equations… <ul><li>Means we are solving equations for a specific variable, but won’t get a numerical answer like before. Instead of getting x = 2, we might get x = 6 + 5y. </li></ul><ul><li>Means “getting a letter by itself”. If we are solving an equation for y, we want the equation to say y = when we are done. </li></ul><ul><li>Still means we use inverse operations! </li></ul>
3. 3. Examples of Solving Literal Equations <ul><li>Solve I = prt for r. </li></ul><ul><li>This means we want to have an equation that says r =. </li></ul><ul><li>To get r by itself, we would divide by p and t. </li></ul><ul><li>I = prt </li></ul><ul><li>pt pt </li></ul><ul><li>r = I </li></ul><ul><li>pt </li></ul><ul><li>Solve 3x + 2y = -16 for y. </li></ul><ul><li>This means we want to get y by itself. </li></ul><ul><li>3x + 2y = -16 </li></ul><ul><li>-3x -3x </li></ul><ul><li>2y = -3x – 16 </li></ul><ul><li>2 2 2 </li></ul><ul><li>y = -3/2x – 8 </li></ul>
4. 4. More Examples <ul><li>Solve 5x – 20y = -40 for x. </li></ul><ul><li>This means we want to get x by itself. </li></ul><ul><li>5x – 20y = -40 </li></ul><ul><li>+20y +20y </li></ul><ul><li>5x = 20y – 40 </li></ul><ul><li>5 5 5 </li></ul><ul><li>x = 4y – 8 </li></ul><ul><li>Solve -3x – 8y = -16 for y. </li></ul><ul><li>This means we want to get y by itself. </li></ul><ul><li>-3x – 8y = -16 </li></ul><ul><li>+3x +3x </li></ul><ul><li>-8y = 3x – 16 </li></ul><ul><li>-8 -8 -8 </li></ul><ul><li>y = -3/8x + 2 </li></ul>
5. 5. More About Literal Equations <ul><li>Being able to “rearrange” equations is very important throughout Algebra I and other math classes. </li></ul><ul><li>You will have to be able to solve for y in our slope modules, because y = mx + b is slope-intercept form. </li></ul><ul><li>You will have to be able to solve formulas for given variables in Geometry so that you can correctly find the answer to a problem. </li></ul>
6. 6. Examples of Problems that Use Literal Equations <ul><li>Direct variation can be modeled by the equation y = kx, where k is a constant (a regular number). Jose is making cupcakes, and the number of eggs needed varies directly as the cups of flour needed. If 5 cups of flour are needed when using 8 eggs, find k (the constant of variation), if x represents the number of eggs and y represents the cups of flour. </li></ul><ul><li>First, solve y = kx for k (because that’s what you want to know). </li></ul><ul><li>x x </li></ul><ul><li>y/x = k </li></ul><ul><li>Then, plug in 5 for y (flour) and 8 for x (eggs). </li></ul><ul><li>5/8 = k Done! </li></ul>
7. 7. Another Example <ul><li>Bricklayers use the formula N = 7LH to estimate the number of bricks N needed to build a wall of length L and height H. What is the height of a wall that is 30 feet long and requires 2310 bricks to build? </li></ul><ul><li>First, solve your equation for H, since height is what we are trying to find. </li></ul><ul><li>N = 7LH </li></ul><ul><li>7L 7L </li></ul><ul><li>H = N </li></ul><ul><li>7L </li></ul><ul><li>Then, plug in 2310 for N (# of bricks) and 30 for L (length). </li></ul><ul><li>H = 2310 = 2310 = 11 </li></ul><ul><li>7(30) 210 </li></ul><ul><li>The height of the wall is 11 feet. </li></ul>
8. 8. Some Extra Practice for You! <ul><li>Here’s a website with some examples you can use to check your understanding. Click the drop-down menus that say “Answer” and you can get helpful hints: </li></ul><ul><li>http://www.regentsprep.org/Regents/math/ALGEBRA/AE4/litPrac.htm </li></ul>