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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