Terms and Definitions
What is the difference between an expression and an equation?
Solve the equation:
4x = 20
4x = 20
/4 / 4
x = 5
Solve the equation:
3x + 5 = 14
3x + 5 = 14
-5 -5
3x = 9
/3 /3
x = 3
The sum of 12 and a number is 48. What is the number?
x + 12 = 48
x = 36
What term is used to describe an unknown number represented by a letter?
Variable
Solve the equation:
-3y = 27
-3y = 27
/(-3) /(-3)
y = -9
Solve the equation:
2x - 7 = 19
2x - 7 = 19
+7 +7
2x = 26
/2 /2
x = 13
Josh is three times as old as his sister, Haley. The product of their ages is 27. How old is Josh?
3x = 27
x = 9
What is a coefficient?
The number in front of the variable.
Solve the equation:
8a = -16
8a = -16
/8 /8
a = -2
Solve the equation:
4a - 12 = 8
4a - 12 = 8
+12 +12
4a = 20
a = 5
The product of 4 and a number decreased by 7 is 17. What is the number?
4x - 7 = 17
x = 6
What do you call something that is straight or forms a straight line?
Linear
Solve the equation:
x - 2 = 7
x - 2 = 7
+2 +2
x = 9
Solve the equation:
7 - 2y = 5
7 - 2y = 5
-7 -7
-2y = -2
/(-2) /(-2)
y = 1
The sum of twice a number and 5 is -13. What is the number?
2x + 5 = 13
x = -9
What does it mean to "solve an equation?"
Isolate the variable
or
Solve for the variable/unknown number
Solve the equation:
3 + x = 6
3 + x = 6
-3 -3
x = 3
Solve the equation:
-y + 6 = 6
-y + 6 = 6
-6 -6
-y = 0
/(-1) /(-1)
y = 0
The length of a rectangle is 6 more than twice its width. If the length is 20, what is its width?
2x + 6 = 20
x = 7