An Equation is a mathematical sentence with an equal sign.

 

A Variable is a letter representing a number.

 

x = 3

 

2 + x = 2 + 3 = 5

x = 8

 

2x 4 = 4

 

16 4 = 4

To solve one-step equations use the inverse operation. Addition is the inverse of subtraction and vice versa. Multiplication is the inverse of division and vice versa.

 

Variables are used when the equation ( or mathematical sentence) stays the same, but the numbers (or values) change.

 

Once you have solved an equation, use a formal check to make sure your solution is correct.

Example: x + 4 = -12

The inverse operation is subtraction of 4 from both sides.

x + 4 – 4 = (-12) – 4

x = -16

?

Check:(-16) + 4 = -12

-12 = -12

Example: d – 8 = -15

The inverse operation is addition of 8 to both sides.

d – 8 + 8 = -15 + 8

d = -7

?

Check: (-7) – 8 = -15

-15 = -15

Example: -4c = 44

The inverse operation is division of each side by -4.

-4c (-4) = 44(-4)

c = -11

?

Check: (-4) x (-11) = 44

44 = 44

Example: F8 = -4

The inverse operation is multiplication of each side by 8.

8 x f8 = (-4) x 8

f = -32

?

Check: (-32)8 = -4

-4 = -4

Example: Jack Nickles is behind in a golf tournament. He currently is at – 1 stroke. The leader John Weekly is at – 8 strokes. What score does Jack need on the last hole to win the tournament?

 

Write an equation to represent this problem and then solve it.

ANSWER: j + (-1) = -8

The inverse operation is subtraction of – 1 from both sides.

 

j + (-1) – (-1) = (-8) – (-1)

j = -7

?

Check: (-7) + (-1) = -8

-8 = -8
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