1.6 Introduction to Solving Equations Objectives: Write and solve a linear equation in one variable. Solve a literal equation for a specified variable.

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Presentation transcript:

1.6 Introduction to Solving Equations Objectives: Write and solve a linear equation in one variable. Solve a literal equation for a specified variable. Standard: D Formulate equations to model routine and non-routine problem.

An equation is a statement that two expressions are equal. A variable is a symbol that represents many different numbers in a set of numbers. Any value of a variable that makes an equation true is a solution of the equation.

IV. Solve Multi-Step Equations Simplify each side of the equation  Distribute  Combine Like Terms Add/subtract the smallest variable term (if there are variables on both sides) Solve the resulting one or two step equation

IV. Solve Multi-Step Equations Ex 1. –2x –7 = 9 Ex 2. 4x + 80 = -6x Ex 3. 3x – 8 = 2x + 2

Solve each equation. 1. 4x + 12 = x/5 + 3 = – 5x = x = -2x x + 80 = -6x 6. 3x + 1 = 1/2 7. 3x – 8 = 2x x – 3 = x /6 x + 3/2 = = 1/2 x /5 x + 12 = x – 5 = -3/2 x + 5/ /3 x – 4/3 = -1/6 x /5x + 6/5 = x - 3

III. An equation may also be solved by graphing!! Type it in y =. Use trace to find the point. Ex 1. Solve 3.24x – 4.09 = -0.72x by graphing. Type into your graphing calculator: Left side of equation:Right side of equation: y 1 = 3.24x – 4.09y 2 = -0.72x

III. An equation may also be solved by graphing!! Type it in y =. Use trace to find the point. Ex 2. Solve 2.24x – 6.24 = 4.26x – 8.76 by graphing. Left side of equation:Right side of equation: y 1 = 2.24x – 6.24 y 2 = 4.26x x = 1.25

II. Substitution If a = b, you may replace a with b. Ex 1. The relationship between the Celsius temperature, C, and the Fahrenheit temperature, F, is given by F = 9/5 C Find the Celsius temperature that is equivalent to 86  F.

II. Substitution Using the equation given in Example 1, find the Celsius temperature that is equivalent to 122  F.

V. Literal Equations An equation that contains two or more variables. Formulas are examples of literal equations. 1. ½ bh = A for b 2. P = 2l + 2w for w

V. Literal Equations 3. A = ½ h(b 1 + b 2 ) for b 2 Solve for the indicated variable: 4. A = ½ h(b 1 + b 2 ) for h 5. y = (u + 1)/(u + 2) for u 6. ax + b = cx + d for x 7. ax + b = cx + d for d 8. I = P(1 + rt) for r 9. I = P(1 + rt) for t 10. y = ½ xv for v

Writing Activities: Solving Equations 9). Solve 5x – 1 = 3x – 15. Explain each step, and include the Properties of Equality that you used. 10). Explain how you can verify that 3(2x + 5) = 9 + 3x and x = -2 are equivalent equations.

Homework Integrated Algebra II – Section 1.6 Level A Honors Algebra II – Section 1.6 Level B