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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Using Addition and Subtraction

After studying this lesson, you will be able to:

Solve equations using addition and subtraction.

A mathematical statement that contains an equal sign is called an equation .

Steps for Solving Equations:

1. Remove parentheses by multiplying (this step is not always necessary)

2. Collect like terms on each side of the equal sign

3. Isolate the variable by undoing the operation

4. Check by substituting the solution into the original equation

The equal sign divides equations into 2 parts or 2 sides. Equations are like balance scales. Whatever is done to one side, must be done to the other side in order to maintain equality or balance.

Example 1

z + 6 = -9	There are no parentheses to be removed and no likes terms to collect
z + 6 - 6 = -9 - 6	To isolate the variable, we "undo" the +6 by subtracting 6 from each side
z = -15

Check:

substitute -15 for z in the original equation

(-15) + 6 = -9

-9 = -9

Example 2

x - (-4) = 10	There are no parentheses to be removed and no likes terms to collect
x + 4 = 10	Since there are 2 negative signs, we "add the opposite" to avoid confusion
x + 4 -4 = 10 -4	To isolate the variable, we "undo" the +4 by subtracting 4 from each side
x = 6

Check:

substitute 6 for x in the original equation

6 - (-4) = 10 (remember to "add the opposite")

10 = 10

Example 3

p - (-2) = -2	There are no parentheses to be removed and no likes terms to collect
p + 2 = -2	Since there are 2 negative signs, we add the opposite to avoid confusion
p + 2 -2 = -2 -2	To isolate the variable, we undo the +2 by subtracting 2 from each side
p = -4

Check:

substitute -4 for p in the original equation

(-4) - (-2) = -2 (remember to add the opposite)

-4 + 2 = -2

-2 = -2

Example 4

x + (-21) = 5.3	There are no parentheses to be removed and no likes terms to collect
x + (-21) + 2.1 = 5.3 + 2.1	To isolate the variable, we "undo" the -2.1 by adding 2.1 to each side
x = 7.4

Check:

substitute 7.4 for x in the original equation (7.4) + (-2.1) = 5.3

5.3 = 5.3