Vocabulary
A statement that two expressions are equal.
Equation
Identify what operation needs to be used to solve
27 + x = 9. State the answer.
We must subtract 27 from both sides of the equation; x = -18
In no particular order, we need to do these two steps in order to solve the following equation:
2x + 5 = 71
- Subtract 5 from both sides of the equation
- Divide both sides of the equation by 2
OR
-Divide both sides of the equation by 2
-Subtract 5/2 from both sides of the equation
|x - 2| = 18
x = 20, x = -16
IN ORDER, these two steps can be used to solve for p in the following equation:
np - m = h
First, add m on both sides of the equation. Then, divide both sides of the equation by n
Two operations that undo each other
Inverse operations
Identify what operation needs to be used to solve
-5x = 125; State the answer
We must divide both sides of the equation by a -5; x = -25
x = 22
|2x + 5| = 35
x = 15, x = -20
y + z = x; Solve for y
y = x - z
A value that makes an equation true
Solution
0.5 - x = -3.5
x = 4
(x/4) + 2 = -4
x = -24
|3x - 2| + 12 = 8
NO SOLUTION! Absolute value is always nonnegative
bh + n = m; Solve for b
b = (m-n)/h
Equation that has TWO or more variables.
Literal equation
Identify what operation needs to be used to solve
x/2 = -46; State the answer.
We must multiply both sides of the equation by 2; x = -92
-2(x - 3) = 6 - 2x
Infinitely many solutions!
2|2x - 7| - 5 = 45
x = 21, x = -9
xy - xz = 10; Solve for x
x = 10/(y - z)
Shows how one variable is related to one or more variables
Formula
Identify what operation needs to be used to solve
x + (2/7) = 8; State the answer.
We must subtract 2/7 from both sides of the equation; x = 54/7 ( or 7 and 5/7)
5 (2 - 2x) = 2(x - 9)
x = 7/3
|5x + 2| / 2 + 20 = 20
x = -2/5
The area of a trapezoid is
A = (1/2)*h*(b1 + b2); Solve for b2
b2 = (2A - hb1)/h