Mathematical Relationships - SAT Math

Substitute in the expression:

To solve for x we need to make two separate equations. Since it has absolute value bars around it we know that the inside can equal either 7 or -7 before the asolute value is applied.

To simplify, we must first simplify the absolute values.

Now, combine like terms:

The absolute value of a number is the points away from zero on a number line.

Since this is a countable value, you cannot count a negative number.

This makes all absolute values positive and also make the statement above false.

Rewrite the quadratic equation in standard form by subtracting from both sides:

Factor this as

where the squares represent two integers with sum and product 14. Through some trial and error, we find that and work:

By the Zero Product Principle, one of these factors must be equal to 0.

If then ;

if then .

The given equation has solution set , so we are looking for an absolute value equation with this set as well.

This equation can take the form

This can be rewritten as the compound equation

Adding to both sides of each equation, the solution set is

and

Setting these numbers equal in value to the desired solutions, we get the linear system

Adding and solving for :

Backsolving to find :

The desired absolute value equation is .

Step 1: Evaluate ...

Step 2: Apply the minus sign inside the absolute value to the answer in Step 1...

Step 3: Define absolute value...

The absolute value of any value is always positive, unless there is an extra negation outside (sometimes)..

Step 4: Evaluate...

Divide both sides by negative three.

Since the lone absolute value is not equal to a negative, we can continue with the problem. Split the equation into its positive and negative components.

Evaluate the first equation by subtracting one on both sides, and then dividing by two on both sides.

Evaluate the second equation by dividing a negative one on both sides.

Subtract one on both sides.

Divide by 2 on both sides.

The answers are:

Follow the correct order of operations: parenthenses, exponents, multiplication, division, addition, subtraction.

First, evaluate any terms in parenthesis.

Next, evaluate the exponent.

Divide.

Finally, add.

Follow the correct order of operations: parentheses, exponents, multiplication, division, addition, subtraction. (This is typically abbreviated as PEMDAS. Note that both multiplication and division, and addition and subtraction, are equal to each other in terms of rank, so when both are present, solving the equation proceeds from left to right).

First, simplify anything in parentheses.

Next, simplify any terms with exponents.

Now, perform multiplication.

Since all we are left with is addition and subtraction, we perform simplification from left to right.

Thus, our answer is:

In modulo 7 arithmetic, a number is congruent to the remainder of its division by 7.

Therefore, since and ,

,

and the correct response is 3.

To solve , make sure the digits are aligned with the correct placeholder. It is also possible to add term by term.

The correct answer is:

Step 1: Recall PEMDAS...

Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Step 2: Perform the evaluation in separate pieces...

Step 3: Replace the values and keep the signs..

Step 4: Evaluate:

Add all the ones digits.

Add the tens digits with the two as the carryover.

Combine this value with the ones digit of the first number.

The answer is:

Add the ones digits.

Add the tens digits with the tens digit of the previous number as carryover.

Repeat the process with the hundreds digits.

Combine this number with the ones digits of the previous calculations.

The answer is:

Using the properties of logarithms

and ,

we simplify as follows:

A set with elements has subsets.

Solve:

In order to solve this problem, covert 27 to the correct base and power.

Since , the correct answer is .

When an exponent is raised by another exponent, we just multiply the powers.

When adding exponents, we don't add the exponents or multiply out the bases. Our goal is to see if we can factor anything. We do see three . Let's factor.

Remember when multiplying exponents, we just add the powers.

Another way to write this is . The only number that makes is .