GRE Math : Algebra
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Example Questions
Example Question #41 : Equations / Inequalities
Solve for 
First combine like terms. In this case, 4x and 9x can be added together:
13x + 13 = 0
Subtract 13 from both sides:
13x = -13
Divide both sides by 13 to isolate x:
x = -13/13
x = -1
Example Question #51 : How To Find The Solution To An Equation
Ben is walking three dogs that weigh an average of 75 pounds each. Ben begins to walk a fourth dog, and the average weight of the dogs decreases to 70 pounds. What is the weight in pounds of the fourth dog?
The total weight of the first three dogs is 225 pounds. This amount, plus the weight of the fourth dog, divided by total number of dogs, is the new average weight:
Example Question #42 : Equations / Inequalities
Pets Plus makes bird houses. Their monthly fixed expenses are $750. The cost for each bird house is $15. The bird houses sell for $40.
What is the monthly break-even point at Pets Plus?
Let 
The break-even point is where the revenue is the same as the costs:
Solve for 
Therefore, Pets Plus must sell 30 bird houses to break-even.
Example Question #51 : How To Find The Solution To An Equation
Pets Plus makes bird houses. Their monthly fixed expenses are $750. The cost for each bird house is $15. The bird houses sell for $40.
If Pets Plus sells 50 bird houses, what is the profit?
Let 
Substituting in 50 for 
Example Question #52 : How To Find The Solution To An Equation
George is three times older than Joey. The sum of their ages is 16. What is the product of their ages?
Let 
Then the equation to solve becomes 
Therefore, Joey is 4 years old and George is 12 years old, so the product of their ages is 48.
Example Question #53 : How To Find The Solution To An Equation
Three consecutive even numbers add to 42. What is the middle number?
Let 
Then the equation to solve becomes 
Thus 
Example Question #54 : How To Find The Solution To An Equation
Consider the following equation:
Which of the following must be true?
The quantity inside the absolute value brackets must equal either 
To solve the first equation, add 9 to both sides:
Subtract 
This is the first solution. Now let's look at the second equation. The distributive law gives us:
Add 9 to both sides:
Add 
Divide both sides by 3:
Therefore, 
Statement 
Statement 
Finally, statement 
Example Question #51 : How To Find The Solution To An Equation
If
then
Divide both sides by 300 to get 
Example Question #151 : Algebra
If b – 3 = a, then (a – b)2 =
The answer cannot be determined from the given information.
–3
9
3
–9
9
The quantity can be regrouped to be –3 = a – b. Thus, (a – b)2 = (–3)2 = 9.
Example Question #333 : Equations / Inequalities
Solve for x: x2 + 4x = 5
None of the other answers
-1
-5 or 1
-1 or 5
-5
-5 or 1
Solve by factoring. First get everything into the form Ax2 + Bx + C = 0:
x2 + 4x - 5 = 0
Then factor: (x + 5) (x - 1) = 0
Solve each multiple separately for 0:
X + 5 = 0; x = -5
x - 1 = 0; x = 1
Therefore, x is either -5 or 1
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