A linear equation is one that can be expressed in the form: Ax + B = 0 Linear equations are also called first degree equations because a linear equation consists of polynomial expressions in which the highest degreed term is one.
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Definition | ||||||
Examples |
EXAMPLES OF LINEAR EQUATIONS |
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Example 1 |
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Example 2 |
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2(x - 4) + 5x = -22 |
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Solving |
STEPS TO SOLVE A LINEAR EQUATION |
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Sample Problems |
Sample Problem 1 |
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2(x - 4) + 5x = - 22
2x - 8 + 5x = - 22 7x
- 8 = - 22 7x = - 14
x = - 2 CHECK: 2(x - 4) + 5x = - 22 2(-2 - 4) + 5(-2) = - 22 (?) 2(-6) + 5(- 2) = - 22 -12 - 10 = - 22 -22 = - 22 ü |
Simplify
the algebraic on each side. Here we begin by removing the
parentheses.
Isolate the variable to one side. Here, add 8 to both sides. Divide both sides by the coefficient of the variable. This is the
proposed solution. Now check in the original equation to verify. |
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Sample Problems |
Sample Problem 2 |
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5(3x) = 2x - 78 15x
= 2x - 78 13x = - 78 13x
= - 78 x = - 6 CHECK
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Multiply both sides of the equation by 10 to clear all fractions.
Isolate the variable to one side
CHECK Replace the
solution in for the variable where ever the variable appears. |
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