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
Find the area and perimeter of a rectangle with side lengths 2 and (x + 6)
Perimeter = 16 + 2x units
Area = 2x + 12 sq. units.
Combine like terms
-12x + x + 5 + 2x + 7
-13x + 12
or 12 - 13x
Solve for x.
−41 = −18 − (3 − 4x)
x = -5
Solve for x
48 < -8x
x <-6
Addition is the inverse of division.
False
What is the inequality to match a graph that has a OPEN circle on 4 and an arrow to the LEFT?
x < 4
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
Draw the graph for the inequality
x > -4
see graph
Distribute, then Combine like Terms
6(-5x + 1) -3(4x - 12)
-42x + 42
Solve for n.
-15 - 5n = 3n + 41
n = -7
Solve for k.
3k + 23 < 7k - 41
16 < k
or k > 16
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.
Write the verbal sentence as an equation then solve. Graph the answer!
A number minus six is at least negative 14
n - 6 >(or equal to) -14
n >(or equal to) -8
Check graph
If a square has sides x + 4 and the perimeter is 64 units, what is the value of x?
12
Solve for y.
18y − 9 = 5(2y + 3)
y = 3
Solve for y.
-2(5y - 12) > 6 - y
y < 2
or 2 > y
Given -4 > -2c -14, the solution is: c <-5
Show all work.
FALSE
c >-5 (double MDNNSS)
Write the verbal sentence as an inequality, then solve AND graph.
14 less than negative 3 times a number IS LESS THAN 10 plus 5 times the number
-3n - 14 < 10 + 5n
n > -3