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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 Equations

You will generally find the last operation is the first thing to undo. Imagine you are computing the equation on a calculator. The last operation you would type is likely to be the first operation to undo. Letâ€™s look at a really big and messy example; try to spot how weâ€™re working backwards to undo it!

Big Messy Example:

Solve for x: 2(x - 1)2 + 3 = 21

Solution:

 Subtract 3 from both sides: 2(x - 1)2 + 3 - 3 = 21 - 3 or: 2(x - 1)2 = 18 Divide both sides by 2: or: (x - 1)2 = 9 Square root of both sides: or: x - 1 = 3 Finally add 1 to both sides: x + 1 - 1 = 3 + 1 or: x = 4

Check:

Substitute 4 into the original equation:

2â€¢(4-1)2 + 3 = 21

2â€¢32 + 3 = 21

2â€¢9 + 3 = 21

21 = 21 Yes!