Combining Like Terms
Combine the like terms
x + 2x =
3x
Solve for x.
x + 15 = 22
x = 7
Is this expression linear? Why or why not?
3x2 + 5
No, because the expression has an exponent greater than 1.
Write an algebraic expression
You give an 18% tip for a meal. What expression represents the total cost with tip?
Let m = the cost of the meal
y is the total cost
y = m + 0.18m
y = m(1 + 0.18)
y = 1.18m
Variable
In algebra, a variable is a letter or symbol used to represent an unknown quantity
Combine the like terms
9m - 7m + 13 =
2m + 13
Solve for x.
x + 2.7 = 4.3
x = 1.6
Is this expression linear? Why or why not?
8xy
No, because it has more than 1 variable
Write an algebraic expression
A pair of shoes sells for 1/4 off. What expression represents the total cost after the discount?
Let s = the original cost of the shoes ; y = total cost
y= s -1/4s
y= s(1 − 1/4 )
y = 3/4s
Like terms
Like terms are parts of an algebraic expression that have the same variable raised to the same power.
Combine the like terms
4a + 8b
4a + 8b
Solve for x.
5x = 75
x = 15
Is this expression linear? Why or why not?
4y
Yes, because it is the product of a constant and a single variable raised to the first power.
Write an algebraic expression
A store discounts a new bike by 35% . What expression represents the total cost?
Let b = the original price of the bike; y = total cost
y = b − 0.35b
y = b(1 − 0.35)
y = 0.65b
Numeric Coefficient
A numeric coefficient is a number multiplied by a variable expression.
For example, in the expression − 2x, the number − 2 is a numeric coefficient. I
Combine the like terms
-5y + 2y + 0.5f + 3g =
-3y + 0.5f + 3g =
Solve for x.
10x - 4x = 30
x = 5
Is this expression linear? Why or why not?
-1 + 3x - 10x + 1/2
Yes, because it is the product of a constant and a single variable raised to the first power.
Write an algebraic expression
Katie starts a limousine rental company. As part of her research, Katie discovers that she must charge a 7% sales tax to her customers in addition to her rental fees
Let r = the rental fee; y = total cost
y = r + 0.07r
y = 1.07r
Inverse Operation
Combine the like terms
11s + 0.78s - w =
11.78s - w
Solve for x.
1/2 (x) = 12
x = 24
Is this expression linear? Why or why not?
x3 + x + 7
No, because it contains two variables instead of one.
BONUS POINTS!!!
:)
linear expression
any expression in which each term is a constant.
any expression in which the term is a product of a constant and a single variable raised to the first power.