Vocabulary
A rule in math that is the first step to follow when solving multi-step equations
What is the Distributive Property?
The solution to the equation -12 = 3 -2k -3k is {2} and the check of _____=______ proves this is true.
What is -12 = -12?
One, none, or infinite?
-3x + 8 -5x = 21-8x
What is no solution?
8 + -8x = 21 -8x
Same variable term, different constant
The mistake in this step makes the solution incorrect.
Step 1 12(5 + 2y) = 4y -(5 - 9y)
Step 2 60 + 2y = 4y -5 - 9y
Step 3 60 + 2y = -5 - 5y
Step 4 60 + 2y + 5y = -5 - 5y + 5y
Step 5 60 - 60 + 7y = -5 - 60
Step 6 7y/7 = -65/7
Step 7 y = -65/7
What is Step 2?
_____ is the solution to 1/3(x + 4) - 6 = 2/3(5 – x)
What is 8?
_____ _____ _____ is a rule that means to put together a variable term with the same variable term and constants with constants.
What is Combining Like Terms?
The solution to the equation -3(1 + 6r) = 14 - r is {-1} and the check of _____=_____ proves this is true.
What is 15 = 15?
One, none or infinite?
12 - 8z = -20- 4z
What is one solution?
Different variable term.
Step 1 n/7 - 12 = 5n + 5
Step 2 n/7 - n/7 - 12 = 5n - n/7 + 5
Step 3 -12 = 34n/7 + 5
Step 4 -12 +5 = 34n/7 + 5 - 5
Step 5 -7(7/34) = 34n/7 (7/34)
Step 6 -49/34 = n
What is Step 4
_____ is the solution to 1/9(2m - 16) = 1/3(2m + 4)
What is -7?
A number placed before a variable or parentheses.
What is a Coeffieient?
The solution to the equation -10n + 3(8 +8n) = -6(n-4) is {0} and the check of _____=_____ proves this is true.
What is 24 = 24?
One, none or infinite?
6 + 3m -4 = -5 +3m +7
What is Infinite Solutions?
2 + 3m = 3m + 2
Same variable term, same constant
The mistake in this step makes the solution incorrect.
Step 1 9 - 7w = 8w - 3 + 11
Step 2 9 - 7w = 8w + 8
Step 3 9 - 7w + 7w = 8w + 7w + 8
Step 4 9 - 8 = 15w + 8 - 8
Step 5 1/15 = 15/15w
Step 6 15 = w
What is Step 6?
_____ is the solution to 2/3(x + 3) = 3x - 5
What is 3?
A ________ _______ is a letter with a coefficient or a letter by itself.
What is a Variable Term?
The solution to the equation -12(x - 12) = -9(1 + 7x) is {-3} and the check of _____=_____ proves this is true.
What is 180 = 180?
One, none, or infinite
4(y-2) + 4 = 2(2y -2)
What is infinite solutions?
4y -8 + 4 = 4y -4
4y - 4 = 4y - 4
Same variable term, same constant
The mistake in this step makes the solution incorrect.
Step 1 -1/2(t + 3) - 10 = -6.5
Step 2 -.5t - 1.5 - 10 = -6.5
Step 3 -.5t - 8.5 = -6.5
Step 4 -.5t - 8.5 + 8.5 = -6.5 + 8.5
Step 5 -.5t/-.5 = 2/-.5
Step 6 t = -4
What is Step 3?
_____ is the solution to 1/2(x + 12) = 3/2(6 + x)
What is -3?
The six steps to solving multi-equations, in order, are: 1. ___ 2. ___ 3.____ 4._____ 5____ 6____.
What is
1. Distribute, if necessary
2. Combine Like Terms
3. Remove variable term from one side, is necessary
4. Remove constant from the variable term side.
5. Solve for variable
6. Check your answer
The solution to the equation -11+10(p+10) = 4-5(2p+11) p is {-7} and the check of _____=_____ proves this is true.
What is 19 = 19?
One, None or infinite
7y -2 = 5y +10 +2y
What is none?
7y-2 = 7y +10
Same coefficient, different constant
The mistake in this step makes the solution incorrect.
Step 1 3(c - 1) + 2(3c + 1) = -(3c +1)
Step 2 3c - 3 + 6c + 2 = -3c -1
Step 3 9c - 1 = -3c -1
Step 4 9c + 3c - 1 = -3c + 3c -1
Step 5 11c -1 + 1 = -1 + 1
Step 6 11c/11 = 0/11
Step 7 c = 0
What is Step 5?
_____ is the solution to 3/4(6 + x) = 4/5(x + 1)
What is 74?