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```Equations Quiz Remediation/Recovery
Directions: The following section illustrates an example of each problem you need to master for this quiz.
Following the example is a written explanation of how the problem was solved. In each equation, remember
the object is to get “x” alone.
Example
Variable
Step 1:
Constant
x – 5 = 12
+ 5
+5
x = 17
This means divide!
Step 1:
x = 3
2
(2) x = 3(2)
2
x = 6
This means multiply!
Step 1:
Step 2:
-3x + 8 = 29
-8
-8
-3x = 21
-3
-3
x = -7
A number attached to a parenthesis means you
multiply that number times each thing inside the
parenthesis!
6 (2x + 3) = 78
Step 1:
Step 2:
Step 3;
6 (2x + 3) =
6(2x) + 6(3) =
12x + 18 =
-18
12x =
12
x =
78
78
78
-18
60
12
5
Explanation of the Steps
Step 1: This problem only has one step because
in order to get “x” (the variable) alone you only
need to get rid of the constant which in this
case is negative because it is subtracted from
the variable. This means you will add 5 to both
sides to get “x” alone. The answer is x = 17.
Step 1: This problem only has one step as well.
On the left, “x” is being divided by 2. This
means we will need to do the inverse operation
of division to get rid of the 2, which is
multiplication. So we multiply each side by 2 to
get “x” alone. The answer is x = 6.
Step 1: In this step you MUST first get rid of
the constant by subtracting it on both side of
the equation. The 8 is subtracted because it
added in the equation. This leaves -3x = 21.
Step 2: In the step the only thing left is the 3
attached to the x. The -3x means the -3 is
multiplied to the x. The inverse of multiplication
is division so we have to divide each side by -3.
The “x” is now alone. The answer is x = -7. The
answer is negative because a positive divided by
a negative is a negative.
Step 1: In step one you MUST first distribute
operations and parenthesis comes first.
Distribute means to multiply each term in the
parenthesis by 6. This gives you 12x + 18 = 78.
Step 2: Next you MUST get rid of the
constant. To do this you subtract 18 on both
sides of the equation. This gives you 12x = 60.
Step 3: Finally you MUST get rid of the 12 in
front of the x. To do this you must divide
because 12x means 12 times x. The final answer
is x = 5.
Example
Before you can begin to get “x” alone, you
must COMBINE LIKE TERMS! Always circle
or box your like terms to make it easier to
see!
- x - 6 - 7x + 20 = -2
Step 1:
- x - 6 - 7x + 20 = -2
Step 2:
Step 3:
-8x + 14 =
-14
-8x =
-8
x =
-2
-14
-16
-8
2
Explanation
Step 1: First you must combine like terms! In
this equation you must combine the –x and -7x,
then you must combine the constants -6 and 20.
It gives you -8x + 14 = -2.
Step 2: In this step you must get rid of the
constant (14). To do this you must subtract 14
from both sides of the equation. This gives you 8x = -16.
Step 3: In this step you must get rid of the -8
attached to the x. To do this you, you divide by
-8. This gives you the answer x = 2 because a
negative divided by an negative is positive.
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