Linear Equations in One Variable

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Linear Equations in One Variable

• 1.4
• SSC 105

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Linear Equation in One Variable
A linear equation in one variable is an equation
that can be written in the form ax b
0 Where a ? 0
For example 2x 1 0, -5x 10 x, 3x
8 2
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Solving Equations
To solve an equation means to find all values
that make the equation a true statement. Such
values are called solutions, and the set of all
solutions is called the solution set.
Solution
Right SideLeft Side??
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Solving equations graphically
Graph both sides of the equation and see where
they intersect!
They intersect at (-2, -20). Since the x value
of this coordinate is -2, then the solution to
the equation is -2.
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Steps to Solve a Linear Equation in One Variable

• Simplify both sides of the equation.
• Clear parentheses.
• Consider clearing fractions or decimals (if any
  are present) by multiplying both sides of the
  equation by a common denominator of all terms.
• Combine like terms.
• Use the addition or subtraction property of
  equality to collect the variable terms on one
  side of the equation.
• Use the addition or subtraction property of
  equality to collect the constant terms on the
  other side of the equation.
• Use the multiplication or division property of
  equality to make the coefficient of the variable
  term equal to 1.
• Check your answer.

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Solve
-5x
-5x
-2
-2
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More Practice SOLVE
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Continued
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And more practice Solve
Multiply by 100
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Conditional Equations
The equation x 4 6 is a conditional equation
because it is true on the condition that x 2.
For other values of x, the statement x 4 6 is
false.
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Contradiction
Solve x 1 x 2
1 2 is a contradiction. This equation has no
solution. And it is NOT linear.
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Identities

• An equation that has all real numbers as a
  solution is an Identity.

For example, X 4 X 4
4 4 is a true statement. Therefore, the
solution is all real numbers.
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LOOK !!!

• At example 6 on page 47.