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Literal Equations, Applications of Linear Equations

Literal Equations, Applications of Linear Equations. Math 021. A literal equation is any equation that contains two or more variables. A literal equation can be thought of as a formula . It is useful in some instances to solve a literal equation for a specific variable .

Literal Equations, Applications of Linear Equations

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1. A literal equation is any equation that contains two or more variables. A literal equation can be thought of as a formula. • It is useful in some instances to solve a literal equation for a specific variable. • Solve V = lwh for w. Then find the value for w if V = 30, l = 3, and h = 2. • Solve I = p + r for p. Then find the value for w if I = 70 and r = 14 • Solve a = b + c – d for c. Then find c when a = -1, b = -2, and d = -3 • Solve s = 2t – 3v for v. Then find v when s = 6, t = -10 • Solve y = mx + b for m. Then find m when y = -8 b = -10, and x = -2

2. Applications of Linear Equations • Steps to successful problem solving: • Gather data & Define the variables – Read the problem, gather the information that you know and more importantly, what you don’t know. Draw a picture if it is helpful. Decide what you are attempting to solve for. • Create an equation – Use the given information to create an equation • Solve the equation – Solve the equation you have formulated using the methods we have learned. • Interpret the solution – Be sure that you have answered the question and that the solution makes sense.

3. Examples – For each problem construct an equation and solve • Twice the sum of a number and ten is the same as four times the number less 6. Create an equation and find the number. • Three times the difference of twice a number and 6 is the same as five times the number increased by -15. Create an equation and find the number. • The sum of three consecutive integers is 321. Find all three integers. • The sum of three consecutive integers is -102. Find all three integers

4. A 40 foot board is cut into 3 pieces. One piece is twice the shortest. Another piece is 4 feet longer than the shortest. Give an equation and find the length of all three pieces. • A 68 foot piece of string is cut into 3 pieces. One piece is five feet longer than the shortest. Another piece is five times the shortest. Give an equation and find the length of all three pieces.

5. Complementary Angles Supplementary Angles

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