# SAT Math : How to find the solution to an equation

## Example Questions

### Example Question #55 : Linear / Rational / Variable Equations

If , what is  in terms of ?

Explanation:

Use inverse operations to isolate x. Working from the outermost part on the left side, we first divide both sides by 5.

To isolate the x term, subtract y from both sides.

Finally, isolating just x, divide both sides by 3.

### Example Question #81 : Equations / Inequalities

If , then, in terms of ,

Cannot be determined

Explanation:

You can solve this problem by plugging in random values or by simply solving for k. To solve for k, put the s values on one side and the k values on the other side of the equation. First, subtract 4s from both sides. This gives 4s – 6k = –2k. Next, add 6k to both sides. This leaves you with 4s = 4k, which simplifies to s=k. The answer is therefore s.

### Example Question #57 : Linear / Rational / Variable Equations

The sum of two consecutive odd integers is 32. What is the value of the next consecutive odd integer?

Cannot be determined

Explanation:

Let  be the smallest of the two consecutive odd integers. Thus,

and it follows that .

We have that 15 and 17 are the consecutive odd integers whose sum is 32, so the next odd integer is 19.

### Example Question #91 : How To Find The Solution To An Equation

John has $50 for soda and he must buy both diet and regular sodas. His total order must have at exactly two times as many cans of diet soda as cans of regular soda. What is the greatest number of cans of diet soda John can buy if regular soda is$0.50 per can and diet soda is \$0.75 per can?

75

51

50

25

50

Explanation:

From our data, we can come up with the following two equations:

0.50R + 0.75D = 50

2R = D

Replace the D value in the second equation into the first one:

0.5R + 0.75 * 2R = 50

0.5R + 1.5R = 50; 2R = 50; R = 25

However, note that the question asks for the number of diet cans, so this will have to be doubled to 50.

### Example Question #81 : Algebra

Translate into an algebraic expression:

One third of the difference of a number and 3 equals five times the number.

Explanation:

You have to form the difference first and must be enclosed in parentheses which gets multiplied by 1/3.  The word "equals" means the "=" symbol

### Example Question #82 : Algebra

Translate into an algebraic expression:

Two fifths of the difference of five times a number and two equals six times the number.

Explanation:

In order to translate the description into an algebraic expression, you must first form the difference , multiply it by , and then set the equation equal to , as follows:

### Example Question #83 : Algebra

Translate into an algebraic expression:

Three halves of the difference between six and eight times a number is equal to four times a number.

Explanation:

In order to translate the sentence into an algebraic expression, first create the difference , multiply it by , and set the expression equal to , as follows:

### Example Question #84 : Algebra

Give the solution set.

The equation has no solution.

or

or

or

or

The equation has no solution.

Explanation:

However, the absolute value of an expression cannot be a negative number. Therefore, this statement is false regardless of the value of , and the original equation has no solution.

### Example Question #85 : Algebra

.

Give the solution set.

or

or

The equation has no solution.

or

or

or

Explanation:

Either  or . Solve them separately:

### Example Question #86 : Algebra

.

Give the solution set.

or

The equation has no solution.

or

or

or