All questions of Inequalities for GRE Exam

The equation simplifies to x > -1.41. -1 is the answer.

3w/2 will become greater than 1 as soon as w is greater than two thirds. It will likewise become less than –1 as soon as w is less than negative two thirds. All the other options always return values between –1 and 1.

Choice a is equivalent because we can say that technically we are multiplying two fractions together: (xy)/z and (5(x + y))/1.  We multiply the numerators together and the denominators together and end up with xy (5x + 5y)/z.  xy (5y + 5x)/z is also equivalent because it is only simplifying what is inside the parentheses and switching the order- the commutative property tells us this is still the same expression.  5x²y + 5xy²/z is equivalent as it is just a simplified version when the numerators are multiplied out.  Choice 5x² + y²/z is not equivalent because it does not account for all the variables that were in the given expression and it does not use FOIL correctly.

Don't forget to switch the inequality direction if you multiply or divide by a negative.

Now that we have the equation in slope-intercept form, we can see that the y-intercept is 6.

Solve the inequality by adding 3 to both sides to get x < 12.  Since it is absolute value, x – 3 > –9 must also be solved by adding 3 to both sides so: x > –6 so combined.

The answer is: 
y − 7 < x + 2y − 14
−y − 7 < x − 14
−1(−y < x − 7)
y> − x + 7
From the equation we can see that the slope is –1.

The question does not give us any specifics about the variables x and y.  

If we substitute the same numbers for x and y (say, x = 1 and y = 1), the two expressions are equal.

If we substitute different number in for x and y (say, x = 2 and y = 1), the two expressions are not equal.

If there are two possible outcomes, then we need more information to determine which quantity is greater. Don't be afraid to pick "The relationship cannot be determined from the information given" as an answer choice on the GRE!

Since x is positive, we can divide both sides of the inequality by x:
x⁴ < 27x ⇒ x³ < 27 ⇒ x < 3 ⇒ x = 1 or 2.

If each pencil sells at 50 cents, x pencils will sell at 50x. The smallest value of x  such that
50x ≥ 1200 + 20x
x ≥ 40

First, we need to find all of the values that are in the set S, and then we need to find the values in T. Once we do this, we must find the numbers in the intersection of S and T, which means we must find the values contained in BOTH sets S and T.
S contains all of the values of x such that 2x + 4 < 8. We need to solve this inequality.
2x + 4 < 8
Subtract 4 from both sides.
2x < 4
Divide by 2.
x < 2
Thus, S contains all of the values of x that are less than (but not equal to) 2. 
Now, we need to do the same thing to find the values contained in T.
-2x + 3 < 8
Subtract 3 from both sides.
-2x < 5
Divide both sides by -2. Remember, when multiplying or dividing an inequality by a negative number, we must switch the sign.
x > -5/2
Therefore, T contains all of the values of x that are greater than -5/2, or -2.5.
Next, we must find the values that are contained in both S and T. In order to be in both sets, these numbers must be less than 2, but also greater than -2.5. Thus, the intersection of S and T consists of all numbers between -2.5 and 2.
The question asks us to find the sum of the integers in the intersection of S and T. This means we must find all of the integers between -2.5 and 2.
The integers between -2.5 and 2 are the following: -2, -1, 0, and 1. We cannot include 2, because the values in S are LESS than but not equal to 2. 
Lastly, we add up the values -2, -1, 0, and 1. The sum of these is -2.
The answer is -2.