PSAT Math : Linear / Rational / Variable Equations
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Example Question #41 : Linear / Rational / Variable Equations
If 11 + 3x is 29, what is 2x?
6
2
36
12
12
First, solve for x:
11 + 3x = 29
29 – 11 = 3x
18 = 3x
x = 6
Then, solve for 2x:
2x = 2 * 6 = 12
Example Question #24 : How To Find The Solution To An Equation
If 2x = 3y = 6z = 48, what is the value of x * y * z?
1536
1024
3072
6144
2304
3072
Create 3 separate equations to solve for each variable separately.
1) 2x = 48
2) 3y = 48
3) 6z = 48
x = 24
y = 16
z = 8
x * y * z = 3072
Example Question #63 : How To Find The Solution To An Equation
If 3|x – 2| = 12 and |y + 4| = 8, then |x - y| can equal ALL of the following EXCEPT:
2
6
14
10
18
14
We must solve each absolute value equation separately for x and y. Remember that absolute values will always give two different values. In order to find these two values, we must set our equation to equal both a positive and negative value.
In order to solve for x in 3|x – 2| = 12,
we must first divide both sides of our equation by 3 to get |x – 2| = 4.
Now that we no longer have a coefficient in front of our absolute value, we must then form two separate equations, one equaling a positive value and the other equaling a negative value.
We will now get x – 2 = 4
and
x – 2 = –4.
When we solve for x, we get two values for x:
x = 6 and x = –2.
Do the same thing to solve for y in the equation |y + 4| = 8
and we get
y = 4 and y = –12.
This problem asks us to solve for all the possible solutions of |x - y|.
Because we have two values for x and two values for y, that means that we will have 4 possible, correct answers.
|6 – 4| = 2
|–2 – 4| = 6
|6 – (–12)| = 18
|–2 – (–12)| = 10
Example Question #42 : Linear / Rational / Variable Equations
No solutions.
No solutions.
Cross multiplying leaves 
Example Question #31 : How To Find The Solution To An Equation
If 
In evaluating, we can simply plug in 4 and 2 for 
Example Question #35 : How To Find The Solution To An Equation
Internet service costs $0.50 per minute for the first ten minutes and is $0.20 a minute thereafter. What is the equation that represents the cost of internet in dollars when time is greater than 10 minutes?
The first ten minutes will cost $5. From there we need to apply a $0.20 per-minute charge for every minute after ten. This gives
Example Question #31 : How To Find The Solution To An Equation
John goes on a trip of 
If we take the units and look at division, 
Example Question #33 : How To Find The Solution To An Equation
With a 
In general, 
The distance is the same going and coming; however, the head wind affects the rate. The equation thus becomes 
Solving for 
Example Question #34 : How To Find The Solution To An Equation
How much water should be added to 
Pure water is 0% and pure solution 100%. Let 
So the equation to solve becomes
and
Example Question #35 : How To Find The Solution To An Equation
Solve 
This problem is a good example of the substitution method of solving a system of equations. We start by rewritting the first equation in terms of 
Solving this equation gives 
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