How to multiply variables - ISEE Upper Level Quantitative Reasoning

Brian eats $\frac{1}{3}$times $\frac{1}{4}$times 12 slices of pizza.

So Brian eats

$\frac{1}{12}$cdot 12=1 slice of pizza.

$\frac{1}{3}$x-14=7

$\frac{1}{3}$x-14+14=7+14

$\frac{1}{3}$x=21

3cdot $\frac{1}{3}$x=21cdot 3

x=63

$4x^{2}$=256

$$\frac{4x^{2}$$}{4}=\frac{256}{4}$

$x^{2}$=64

$$\sqrt{x^{2}$$}=$\sqrt{64}$

x=pm 8

This can be solved using the pattern for the square of a difference:

This can be solved using the pattern for the square of a sum:

This can be solved using the pattern for the square of a sum:

Use the FOIL method:

Substitute for :

First, recognize that raising the fraction to a negative power is the same as raising the inverted fraction to a positive power.

Apply the exponent within the parentheses and simplify. Remember that fractional exponents can be written as roots.

Simplify by taking the roots and canceling common factors.

First, recognize that raising the fraction to a negative power is the same as raising the inverted fraction to a positive power.

Apply the exponent within the parentheses and simplify. The negative in the fraction can be applied to either the numerator or the denominator, but not both; we will apply it to the numerator.

The fraction cannot be simplified further.

Reorder the expression to group like-terms together.

Simplify by combining like-terms.

If the product of three consecutive numbers is 990, then the smallest number can be found by plugging in each answer choice into the scenario to see whether it is correct.

If we plug in 9 as the smallest number, then the two consecutive numbers would be 10 and 11.

Given that 9 times 10 times 11 equals 990, that is the correct answer.

In order to solve this problem, the price of $50 must be discounted by 10% until we get to a price of $38 or less.

The first class is 50.

The second class, being 10 percent less than the previous one, is

The third class, being 10 percent less than the previous one, is

The fourth class, being 10 percent less than the previous one, is

Therefore, the answer is 4.

If x is equal to , then the equation could be written as follows:

Given that is a positive number, is a possible value of .

The first step is to simplify the values in the parentheses:

Multiply the binomials using the FOIL method - first, outer, inner, last - then combine like terms:

and ; also, by the Power of a Product Principle:

.

and are both positive, so, substituting:

.

Again, using substitution:

Simplify the following expression

Let's begin by multiplying our coefficients:

Next, we need to realize that we can combine our x's by adding the exponents.

Put it all together to get:

Simplify the following:

To begin, our coefficient will not change. We have just one integer (the 9) and nothing to multiply it by.

To combine our exponents, we will add them. This is because we are multiplying them

Put it together to get: