Simplifying Expressions
Distribute
3(4x + 2)
12x + 6
Solve for x.
2(x - 5) = 2
x = 6
Solve for c.
c - 11 > 22
c < 33
or 33 > c
We use inverse operations to solve equations and inequalities.
True
What is the first step in the following equation?
4x+8=32
Subtract 8
Combine like terms
-12x + x + 5 + 2x + 7
-13x + 12
or 12 - 13x
Solve for x.
(x/10)-16=-4
x = 120
Solve for x
48x < 8
x < 1/6
Addition is the inverse of division.
False
In the following equation 3x + 12 = 14, what is the coefficient?
3
What is a shorter way to write x+x+x+x+x?
5x
Solve for x.
3x −1 − 7x = −33
What is:
x = 8
Solve for x
3x + 2 < -4
x < -2
or -2 > x
We use a closed circle to represent the inequalities < and >
False
Solve for k.
-2k < 6
k > -3
or -3 < k
Distribute, then Combine like Terms
6(-5x + 1) -3(4x - 12)
-42x + 42
Solve for n.
19x+10=86
n = 4
Solve for k.
-2k+7<15
k>-4
or -4<k
Inequalities only have one solution, just like equations.
False. Inequalities have infinitely many solutions.
What is the first step to simplifying
2x + 3(x + 4).
Below is a students response. Is the student correct?
The first step to simplifying the expression is to get rid of the parenthese by combining the like terms inside the parentheses. This expression
2x + 3(x + 4)
No, x and 4 are not like terms.
1st step: Distribute the 3 to every term inside the parentheses.
Is 3x + 6 equivalent to 3(x+2)?
Yes--they are equivalent expressions by the distributive property.
Solve for y.
-8(2y+3)=40
y = -4
Solve for y.
(y/3)-(-2)<16
y < 42
or 42 > y
Given c + 4 > 14
We use the inverse operation of subtraction to solve the inequality.
FALSE
When solving an inequality, there's a specific type of number and operation(s) that change a symbol in the inequality. What is that rule and what symbol changes because of it?
The rule is if you multiply or divide by a negative number, you must flip the inequality sign.