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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Solving Linear Equations

Example 1

Solve: 3(2x - 6) = -2(x + 4) - 50.

 Solution Step 1 Remove parentheses. Distribute 3 and distribute -2. Step 2 On each side of the equation, combine like terms. Combine -8 and -50. Step 3 Isolate the variable. Add 18 to both sides. Simplify. Add 2x to both sides. Simplify. Divide both sides by 8. 3(2x - 6)   6x - 18   6x - 18   6x - 18 + 18 6x 6x + 2x 8x = - 2(x + 4) - 50  = - 2x - 8 - 50   = - 2x - 58   = - 2x - 58 + 18 = - 2x - 40 = - 2x - 40 + 2x = - 40 Simplify. Step 4 Check the solution in the original equation. We leave the check to you. x = -5

The solution is x = -5.

Note:

We can also solve 6x - 18 = - 2x - 58 by first adding 2x to both sides:

 6x - 18 + 2x 8x - 18 8x - 18 + 18 8x x = - 2x - 58 + 2x = - 58 = - 58 + 18 = - 40 = -5

The solution of the previous example was a unique real number.