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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: 2.8.11 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 + 32. 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 + 3.65 by graphing.
Type into your graphing calculator:
Left side of equation: Right side of equation:y1 = 3.24x – 4.09 y2 = -0.72x + 3.65
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 – 6.24 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 EquationsEx 1. –2x –7 = 9
Ex 2. 4x + 80 = -6x
Ex 3. 3x – 8 = 2x + 2
V. Literal Equations
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