 # 1.6 Introduction to Solving Equations

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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.

I. Properties of Equality
For real numbers a, b, c: Reflexive Property a = a Symmetric Property If a = b, then b = a. Transitive Property If a = b and b = c, then a = c. Addition Property If a = b, then a + c = b + c. Subtraction Property If a = b, then a – c = b – c. Multiplication Property If a = b, then ac = bc. Division Property If a = b, then a  c = b  c, c  0.

I. Properties of Equality
Tell which Properties of Equality you would use to solve each equation. 1). 52 = -2.7x – 3 Addition Property of Equality Division Property of Equality 2). x = x + 22 2 Multiplication Property of Equality Subtraction Property of Equality

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

Solve 3x – 8 = 5x – 20. Check your solution by using substitution.
Check the solution by substitution:

Solve 7 – 6x = 2x –9. Check your solution by using substitution.

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: y1 = 3.24x – y2 = -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: y1 = 2.24x – y2 = 4.26x -8.76 x = 1.25

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

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

V. Literal Equations Ex 3. A = ½ h(b1 + b2) for b2

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 Academic Algebra II – Section 1.6 Level B