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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

The techniques shown here should not be attempted until you have become proficient at solving equations by writing out every step. The more efficient techniques shown here are not a requirement of algebra, but they can be a labor-saving tool that will be useful when we solve more complicated problems.

Example

Efficient solutions

Solve each equation.

a) 3x + 4 = 0

b) 2 - (x + 5) = -2(3x - 1) + 6x

Solution

a) Combine steps to solve the equation efficiently.

 3x + 4 = 0 3x = -4 Subtract 4 from each side. x Divide each side by 3.

Check in the original equation:

The solution set is

 2 - (x + 5) = -2(3x - 1) + 6x -x - 3 = 2 Simplify each side. -x = 5 Add 3 to each side. x = -5 Additive inverse property.

Check that -5 satisfies the original equation. The solution set is {-5}.