One & Two-Step Equations
x = -6
Solve & identify the type of solution:
2x + 5 = 5 + 2x
0 = 0
Infinitely Many Solutions
3(x + 4) - 5 = 16
x = 3
3(x - 4) = 2x + 1
x = 13
Emma has 50 marbles and gets 5 more each week. Liam has 80 marbles and gets 2 more each week. After how many weeks will they have the same number of marbles?
50 + 5x = 80 + 2x
x = 10
After 10 weeks, they will have the same amount of marbles.
-12x = 144
x = -12
Solve & identify the type of solution:
3(x + 1) + 1 = -2 + 3x
0 = -2
No Solution
2(3x - 1) + 4x = 5x + 8
x = 2
2x - 5 = x - 3
x = 2
A movie rental store charges a $10 membership fee plus $3 per movie. Another store charges $5 membership plus $5 per movie. After renting how many movies will the total cost be the same?
10 + 3x = 6 + 5x
x = 2
After 2 movies, the cost will be the same
x/4 - 2 = 5
x = 28
3x + 1 + 7x = 2(5x + 1)
1 = 2
No Solution
4(x - 2) - 3(x + 5) = 7
x = 30
4(x - 1) = 2x + 10
x = 7
Two friends are saving for a concert. Ava has $75 and saves $15 per week. Ben has $50 and saves $20 per week. After how many weeks will they have the same amount?
x = 5
After 5 weeks, the two friends will have the same amount of money.
-7x + 2 = 30
x = -4
12 + 2x - x = 9x - 12
One Solution
1 - 3(x - 2) + 5x = 21
x = 7
3/2x + 3 = 5/4x + 1
x = -8
A farmer has 200 pounds of hay and adds 15 pounds each day. Another farmer has 260 pounds of hay and adds 10 pounds each day. After how many days will they have the same amount of hay?
200 + 15x = 260 + 10x
x = 12
After 12 days, the farmers will have the same amount of hay.
2/3x + 5 = -11
x = -24
4(x + 1) - 3 = 3(x + 1) + x - 2
4x + 1 = 4x + 1
Infinitely Many Solutions
5(2x - 1) - 3(x + 4) = 2x + 8
x = 5
5(x + 2) - 3x = 2(x + 7) + 1
x =
Cell Phone Plan A costs $30 plus $12 per gigabyte. Cell Phone Plan B costs $50 plus $8 per gigabyte. After how many gigabytes will the plans cost the same?
30+ 12x = 50 + 8x
x = 5
After 5 gigabytes, the plans will cost the same.