Download 1-5 Variables and Equations

1-5 Variables and Equations
How is solving an open sentence
similar to evaluating an expression?
Vocabulary
• equation – a mathematical sentence that
contains and equals sign (=)
• open sentence – an equation that contains a
variable
• solution – a value for a variable that makes an
equation true
• solving the equation – the process of finding a
solution
Solving and Equation
• Find the solution of 12 – m = 8. Is it 2, 4, or 7?
Value for m
12 - m = 8 True or False?
• Find the solution of 44 + p = 53. Is it 11, 9, or
7?
Value for p
44 + p = 53
True or False?
Multiple-Choice Test Items
• Which value is a solution of 2x + 1 = 7?
A. 6 B. 5 C. 4 D. 3
D
• Which value is the solution of 4x – 1 = 11?
A. 5 B. 4 C. 3 D. 2
C
Solve simple equations mentally.
5x = 30
Think: What number times 5 is 30?
x=6
72
8
d
Think: 72 divided by what number is 8?
d=9
7 x  56
x 8
x 15  40
x  55
Properties of Equality
• Symmetric
– If one quantity equals a second quantity, then the
second quantity also equals the first.
• Ex. If 10 = 4 + 6, then 4 + 6 = 10.
• Transitive
– If one quantity equals a second quantity and the
second quantity equals the third quantity, then
the first equals the third.
• Ex. If 3 + 5 = 8, and 8 = 2(4), then 3 + 5 = 2(4).
Name the property of equality.
• If 5 = x + 2, then x + 2 = 5.
– Symmetric Property of Equality
• If y + 8 = 15 and 15 = 7 + 8, then y + 8 = 7 + 8.
– Transitive Property of Equality
• If z + 6 = 8 and 8 = 2 + 6, then z + 6 = 2 + 6.
– Transitive Property of Equality
• If 3x + 1 = 10, then 10 = 3x + 1
– Symmetric Property of Equality
Translate Sentences Into Equations
• The difference of a number and 10 is
seventeen. Find the number,
• 27
• The quotient of a number and four is nine.
Find the number,
• 36