Two-Step Equations
Solve 3x + 2 = 14
x = 4
-4 + 3x + 6 = 14
x = 4
Sam has twice as many marbles as Max. Together they have 18. How many does Sam have?
2x + x = 18
3x = 18
x = 6 marbles
Is this sequence arithmetic? 3,6,9,12,…
yes
Find the 5th term of a1=3, d=4
19
x/4 + 0.5 = 2
x = 10
2(x - 3) + 5 = 15
x = 8
A baker uses 3/4 cup of sugar for each batch. If she uses 9 cups of sugar, how many batches can she make?
12 batches
Find the common difference: 7.5, 12.0, 16.5, 21.0, ...
+ 4.5
Find the 12th term of a1=10, d=−2.5
-17.5
x = 3
4(x - 3) - 3 = 5x - 7
x = 12
A car travels 150 miles in 3 hours. At that same constant speed, how long will it take to travel 375 miles?
150/3 = 50
375/50 = 7.5 hours
Is this arithmetic? 5,9,13,18,…
No
Write the formula for sequence 5,9,13,17,…
a1 = 5 and d = 4
an = 5 + (n-1)*4
an = 4n + 1
x/3 + 5/6 = 2
7/2
OR
3 1/2
2/3(x-4) + 5 = 3/4x - 1
8x + 28 = 9x - 12
x = 40
A jacket originally costs $80. It is marked down 25% and then taxed at 8% on the sale price. What is the final price (to the nearest cent)?
80*0.25 = 20 --> 80-20 = 60
60*0.08 = 4.80 --> 60 + 4.80
$64.80
The 1st term is 7/2 and d=−3/4. What is the 6th term?
an = a1 + (n - 1)d
a6 = a1 + (6 - 1)d
a6 = 7/2 + 5(-3/4)
a6 = - 1/4
Which term is 70 in the sequence an=4+3(n−1)?
4 + 3(n-1) = 70
3(n-1) = 66
n - 1 = 22
n = 23
5x - 7/4 = 9/2
5/4
Or
1 1/4
0.4(2x - 3) - 1/3(x+6) = 1.2x - 2
x = - 18/11
or
-1.6
Wally picks the same number of apples every day. On the 5th day, he picked 30, and on the 12th day, he picked 72 apples. How many apples will he have picked by his 50th day?
30/5 = 6 and 72/12 = 6
so y=6x
y = 6(50)
y = 300
Sequence: 13, 20, 27, 34,… Find the 45th term.
a1 = 13, d = 7
a45 = 13 + 44(7) = 13 + 308 = 321
The sequence starts 9,15,21,27,…
Which term equals 205?
a1 = 9 and d = 6
an = 9 + (n-1)*6
9 + (n-1)*6 = 205
6(n-1) = 196
n - 1 = 32.7
n = 31.7 --> no term will equal 205