SOLVING LINEAR EQUATIONS

Recall the following:

LINEAR EQUATION - Solve for x in the following equation.

Example 1:

$\displaystyle {\textstyle\frac{3}{4}}$x + $\displaystyle {\textstyle\frac{5}{6}}$ = 5x - $\displaystyle {\textstyle\frac{125}{3}}$

Multiply both sides by the lowest common multiple of 4, 6, and 3, or 12.

12$\displaystyle \left(\vphantom{\frac{3}{4}x+\frac{5}{6}}\right.$$\displaystyle {\textstyle\frac{3}{4}}$x + $\displaystyle {\textstyle\frac{5}{6}}$$\displaystyle \left.\vphantom{\frac{3}{4}x+\frac{5}{6}}\right)$ = 12$\displaystyle \left(\vphantom{5x-\frac{125}{3}}\right.$5x - $\displaystyle {\textstyle\frac{125}{3}}$$\displaystyle \left.\vphantom{5x-\frac{125}{3}}\right)$

Simplify:

12$\displaystyle \left(\vphantom{\frac{3}{4}x}\right.$$\displaystyle {\textstyle\frac{3}{4}}$x$\displaystyle \left.\vphantom{\frac{3}{4}x}\right)$ + 12$\displaystyle \left(\vphantom{\frac{5}{6}}\right.$$\displaystyle {\textstyle\frac{5}{6}}$$\displaystyle \left.\vphantom{\frac{5}{6}}\right)$ = 12(5x) - 12$\displaystyle \left(\vphantom{\frac{125}{3}}\right.$$\displaystyle {\textstyle\frac{125}{3}}$$\displaystyle \left.\vphantom{\frac{125}{3}}\right)$

3(3x) + 2(5) = 60x - 500

9x + 10 = 60x - 500

Subtract 9x from both sides of the equation:

10 = 51x - 500

Add 500 to both sides of the equation:

510 = 51x

Divide both sides by 51:

x = $\displaystyle {\textstyle\frac{510}{51}}$ = 10

The answer is x = 10.

Check the solution by substituting 10 in the original equation for x. If the left side of the equation equals the right side of the equation after the substitution, you have found the correct answer.

You can also check your answer by graphing tex2html_wrap_inline128 (left side of the original equation minus the right side of the original equation). The graph will cross the x-axis at x=10.


If you would like to review another example, click on Example

If you would like to test yourself by working some problems similar to this example, click on Problem.

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Author:Nancy Marcus

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