Variables on ONE side
x - 10 + 3x = 14
x - 10 + 3x = 14
4x - 10 = 14
4x = 24
x = 6
Find the type of solution
7(y + 3) = 5y + 9
7(y + 3) = 5y + 9
7y + 21 = 5y + 9
2y + 21 = 9
2y = 12
y = 6 ; One solution
-6(m + 1) + 18 = 24
-6(m + 1) + 18 = 24
-6m -6 + 18 = 24
-6m + 12 = 24
-6m = 12
m = -2
15 + 6x = 45 + 8x
15 + 6x = 45 + 8x
15 = 45 + 2x
-30 = 2x
-15 = x
-16z + 4z + 15 = -21
-16z + 4z + 15 = -21
-12z + 15 = -21
-12z = -36
z= 3
Find the type of solution:
-13x + 4x -10 = -6 - 4 - 9x
-13x + 4x -10 = -6 - 4 - 9x
-9x - 10 = -10 - 9x
Infinitely many solutions
WRITE AN EQUATION & SOLVE: Julie is 3 years older than her sister. Julie's age is 11 years old. How old is her sister?
n - Julie's sister's age
n + 3 = 11
n = 8
Julie's sister is 8 years old.
16 - 2t = t + 9 + 4t
16 - 2t = t + 9 + 4t
16 - 2t = 5t + 9
16 = 7t + 9
7 = 7t
1 = t
-2x - 6 + 12 = 20
-2x - 6 + 12 = 20
-2x + 6 = 20
-2x = 18
x = -9
Find the type of solution:
5(x + 12) = 7 + 5x
5(x + 12) = 7 + 5x
5x + 60 = 7 + 5x
60 = 7 ; No solution
Find the type of solution:
3x + 5 - x = 2x +7
3x + 5 - x = 2x +7
2x +5 = 2x + 7
5 = 7 ; No solution
4b + 5 = 32 + 5b - 10b
4b + 5 = 32 + 5b - 10b
4b + 5 = 32 -5b
9b + 5 = 32
9b = 27
b = 3
17 -3x -12x + 7 = -36
17 - 3x - 12x + 7 = -36
24 - 3x - 12x = -36
24 - 15x = -36
-15x = -60
x = 4
Find the type of solution:
2(x + 5) - 7 = 3(x - 2)
2(x + 5) - 7 = 3(x - 2)
2x + 10 - 7 = 3x -6
2x + 3 = 3x - 6
3 = x -6
9 = x ; One solution
7k - 8 + 2(k + 12) = 52
7k - 8 + 2(k + 12) = 52
7k -8 + 2k + 24 = 52
9k + 16 = 52
9k = 36
k = 4
17 - 2x = 2x + 5 + 2x
17 - 2x = 2x + 5 + 2x
17 - 2x = 4x + 5
12 - 2x = 4x
12 = 6x
2= x
The 1954 elevation of Mt. Everest was 29,028 ft. In 1999, that elevation was revised to be 29,035 ft. Write and solve an equation to find the change c in elevation of Mt. Everest. Remember to answer in a complete sentence.
29035 - c = 29028 The change in elevation is 7 feet.
Find the type of solution:
4(3x + 1) = 12x + 3
4(3x + 1) = 12x + 3
12x + 4 = 12x + 3
4 = 3 : No solution
Tyler has 4 boxes of apples. Each box has the same number of apples. After Tyler eats 3 apples, there are 109 apples left in the boxes. How many apples were in each box?
a - # of apples in each box
4a - 3 = 109
a = 28
There were 28 apples in each box.
4d − 4 + 16 = 5d − 8 - 17
4d − 4 + 16 = 5d − 8 - 17
4d + 12 = 5d -25
4d + 37 = 5d
37 = d