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1.) 3x – (4 – 2x) = 3(x + 4)
x
2
#
-4
3
5x
-4
3x – 4 + 2x = 3x + 12
5x – 4 = 3x + 12
-3x
-3x
2x – 4 = 12
+4 +4
2x = 16
2
2
x = 8
CA Standards:
4.0: Students simplify expressions before solving linear equations
in one variable. 12.0: Students simplify fractions with polynomials
in the numerator and denominator by factoring both and reducing
them to the lowest terms.
Objective:
Students simplify expressions and use inverse operations to solve
equations.
Agenda
1.) Warm-Up
2.) Lesson – No Solution/All Real Numbers
3.) Worksheet: Solving Linear Equations 1
What about this?
2(6x + 8) = 4(4 + 3x)
12x + 16 = 16 + 12x
-12x
-12x
First, Distribute
Collect like terms? No
Move the smaller variable.
• Do the Opposite!
16 = 16
***Special case***
 If the variables cancel out, and the number is the same on both sides, the
answer is ALL REAL NUMBERS.
 This means no matter what number you substitute for x, the problem
will always work out.
And this?
4(6x + 7) = 8(4 + 3x)
24x + 28 = 32 + 24x
-24x
-24x
28 = 32
?
First, Distribute
Collect like terms? No
Move the smaller variable.
• Do the Opposite!
***Special case***
 If the variables cancel out, and the numbers on the two sides are different,
then there is NO SOLUTION.
 This means no matter what number you substitute for x, the problem
will never work out.
Your Turn!!!
2(8x – 6) = 4(3 + 4x)
16x – 12 = 12 + 16x
-16x
-16x
-12 = 12
Are they the same?
No Solution
First, Distribute
Collect like terms? No
Move the smaller variable.
• Do the Opposite!
NO WAY