Solving for the Variable
Solve:
5x=35
x=7
The pattern follows the rule:
s=4n+1
How many squares are in Figure 7?
4(7)+1=29
Solve:
2x+7=19
2x=12
x=6
Rollerblades cost $4 per hour.
What is the cost for 7 hours?
$28
Solve the inequality and describe how it would look on a number line:
x+6>10
x>4
Number line: open circle at 4, shade to the right
Solve:
3y+6=18
3y=12
y=4
A pattern starts with 5 (term 1) and increases by 4 each time.
Write an algebraic expression for the pattern using n.
4n+1
Solve:
6p+8=50
6p=42
p=7
Rollerblades cost $4 per hour.
Write an equation for the rollerblade cost.
C=4h
Solve the inequality and describe how it would look on a number line:
3x<15
x<5
Number line: open circle at 5, shade to the left
Determine if the equations are equivalent:
2n+6=14
n + 3 = 7
Both give n=4
Yes, they are equivalent.
A pattern follows the rule:
s=3n+4
How many squares are in Figure 15?
3(15)+4=49
Solve:
x/3+5=11
3/x=6
x=18
Bike rental costs $10 + $3 per hour.
How much for 6 hours?
10 + 3(6)
10 + 18 = 28
Solve the inequality and describe how it would look on a number line:
x/2+4≥9
x/2≥5
x≥10
Number line: closed circle at 10, shade right
Solve and compare:
4s−5=11
2s+1=9
Are they equivalent?
First: s=4
Second: s=4
Yes.
A pattern follows the rule:
s=5n−2
How many squares are in Figure 12?
5(12)−2=58
Solve:
y/4−2=6
y/4=8
y=32
If a bike rental costs $10 + $3h, how long did someone ride if the total was $37?
10+3h=37
3h=27
h=9
Solve the inequality and describe how it would look on a number line:
4x−3≤13
4x≤16
x≤4
Number line: closed circle at 4, shade left
A student says multiplying both sides of an equation by 2 creates a new equation.
Will it still be equivalent? Why?
Yes.
Doing the same operation to both sides keeps the solution the same.
A pattern has the following values:
Figure (n) Squares (s)
1 6
2 9
3 12
4 15
What is the pattern rule?
How many squares are in Figure 20?
Pattern rule:
s=3n+3
Figure 20:
3(20)+3=63
Solve:
4x+7=2x+17
2x+7=17
2x=10
x=5
A bowling alley charges $12 to rent shoes plus $4 per game.
A student spent $36 total.
How many games did they play?
Let g = number of games
Equation:
12+4g=36
Subtract 12:
4g=24
Divide by 4:
g=6
They played 6 games.
Solve the inequality and describe how it would look on a number line:
7 < z/4 + 3
4<z/4
16<z
Number line: open circle at 16, shade right