2. 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.

3. 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.

4. 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.

5. 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

6. 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.

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

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

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

10. 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

11. 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

12. 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

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

14. 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

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

16. 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.

18. Homework
Integrated Algebra II – Section 1.6 Level A
Academic Algebra II – Section 1.6 Level B