# Section 1.3 Solving Linear Equations

```Advanced Algebra - Trigonometry
Objective:
SWBAT solve linear equations.
1
Warm Up
Simplify:
1. 8b - 3( 4 – b )
2. -6 (m – 9) + 14m – 20
3. 2 (b + 5) + 3 (2b – 10)
4. -w3 + w2 - 7 w2 - 8w3
5. 7t (t2 + 2) + 9t (t – 2)
2
Vocabulary
Equation: a statement that two expressions are equal.
Ex. x + 2 = 9, x2 – 4x +10 = 0,
Solution: all numbers that make an equation true.
Solution Set: the set of all the solutions of an or condition.
Equivalent Equations: equations with the same solution set
Ex. x + 1 = 5 and 6x + 3 = 27
Linear Equation: a linear equation in one variable has the
form ax + b = c (aka first degree equation)
3
Which of the following are a linear
equations?
a.
3x - 7=12
b. 24x + 5 = 5(x – 2)
c.
2x - 7x2 + 4x3 = 19
d. 12x + 3= -4x-8
e.
4
5
x + 8 = 20
f.
1

= −8
4
Solve an equation with variable on one side.
2
x7  5
3
5
Solve an equation with variable on both sides.
Solve:
8y – 16 = 13y + 9
6
Solve an equation using the distributive
property.
Solve:
4(2x – 9) + 5x = -3(10 – x)
7
Solve an equation with clearing a fraction.
Solve:
2t  4 1
1 7
 t t
3
2
4 3
8
Identity: an equation that is satisfied by every number
Conditional Equation: an equation that is satisfied by some
numbers but not others
Contradiction: an equation that has no solution and the
solution set is an empty set or null set. {0}.
9
Identify the Type of Equation.
Decide whether each equation is an identity, a conditional equation, or
a contradiction. Give the solution set.
a. -2(x + 4) + 3x = x – 8
b. 5x – 4 = 11
c. 3(3x-1) = 9x +7
10
Homework.
Page 440 – Appendix A
# 2-22 evens
11
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