Saturday, November 3, 2012

Solving Linear Equations: Part I


One method for solving a linear equation that looks like 2x + 3 = 13 is to simply guess and check.  What value can I substitute in for x so that the result will be 13?  After some thought it should be easy to see that x must equal 5 because 2 * 5 + 3 = 10 + 3 = 13.  However, guessing at solutions to linear equations becomes very difficult when the numbers are not so nice.  When solving, the idea is to use the properties of equality to isolate the variable.
Tip: We can always check by substituting our solution into the original equation to see if we obtain a true statement.  If you have time on an exam you should always check.
Solve for x.
Word Problem: Maria scored 7 more points than Jose on the first mathematics exam.  If Maria's total score was 95 what was Jose's total. (Set up an algebraic equation and solve it)
Tip: You can save a step if you multiply both sides of the equation by the reciprocal of the coefficient.
When solving, apply the addition or subtraction property of equality first. Next apply the multiplication or division property of equality as needed to isolate the variable.


Solving General Two Step Equations
Steps for solving general linear equations of the form $ ax + b = c$.
$$ 2x + 3 = 13 $$
Add $-3$ on both sides of the equation.
$$ 2x = 10 $$
Divide both sides by $2$.
$$ x = 5 $$
Check: $2(5) + 3 = 10 + 3 = 13$ ✔

Solve for x.

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