Solving Equations

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Enter expression, e.g. (x^2-y^2)/(x-y)

Enter expression, e.g. x^2+5x+6

Enter expression, e.g. (x+1)^3

Enter a set of expressions, e.g. ab^2,a^2b

Enter equation to solve, e.g. 2x+3=4

Enter equation to graph, e.g. y=3x^2-1

Depdendent Variable

Number of equations to solve:

Equ. #1:

Equ. #2:

Equ. #3:

Equ. #4:

Equ. #5:

Equ. #6:

Equ. #7:

Equ. #8:

Equ. #9:

Solve for:

Enter inequality to solve, e.g. 2x+3>4

Enter inequality to graph, e.g. y<3x^2-1

Dependent Variable

Number of inequalities to solve:

Ineq. #1:

Ineq. #2:

Ineq. #3:

Ineq. #4:

Ineq. #5:

Ineq. #6:

Ineq. #7:

Ineq. #8:

Ineq. #9:

Solve for:

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Solving Equations with Addition and Subtraction

You can add or subtract the same number on each side of an equation and the result is an equivalent equation . Equivalent equations have the same solution.

Addition Property of Equality	For any numbers a, b, and c, if a = b, then a + c = b + c.
Subtraction Property of Equality	For any numbers a, b, and c, if a = b, then a - c = b - c.
Solving Equations	To solve an equation means to get the variable (with a coefficient of 1) by itself on one side of the equation. You can do this by undoing what has been done to the variable, using the properties of equality.

Example

Solve .

Solution

The number has been subtracted from x. The opposite of subtracting is adding . Add to each side of the equation. is an equivalent equation. Simplify to obtain x = 1.

Check: Is ? Yes. The solution is 1.

Solving Equations with Multiplication and Division

You can solve a multiplication or division equation by using the multiplication and division properties of equality.

Multiplication Property of Equality	For any numbers a, b, and c, if a = b, then ac = bc.
Division Property of Equality	For any numbers a, b, and c, with c 0, if a = b, then .