### All ACT Math Resources

## Example Questions

### Example Question #1 : Simplifying Expressions

Simplify the result of the following steps, to be completed in order:

1. Add 7*x* to 3*y*

2. Multiply the sum by 4

3. Add *x* to the product

4. Subtract *x –* *y* from the sum

**Possible Answers:**

28*x* + 12*y*

28*x* + 13*y*

28*x* – 13*y*

29*x* + 13*y*

28*x* + 11*y*

**Correct answer:**

28*x* + 13*y*

Step 1: 7*x* + 3*y*

Step 2: 4 * (7*x* + 3*y*) = 28*x* + 12*y*

Step 3: 28*x* + 12*y* + *x* = 29*x* + 12*y*

Step 4: 29*x* + 12*y* – (*x* – *y*) = 29*x* + 12*y* – *x* + *y* = 28*x* + 13*y*

### Example Question #1011 : Algebra

What is the simplified version of the expression:

?

**Possible Answers:**

**Correct answer:**

Use PEMDAS to dictate which operation comes first. Simplify the parentheses:

and

.

Next come exponents:

After that comes multiplication and division left to right:

and

.

Finally, add all the terms together:

### Example Question #32 : Simplifying Expressions

The expression

can be rewritten as:

**Possible Answers:**

**Correct answer:**

To simplify this problem, let’s look at each term individually. ; ; . Thus B is the correct answer.

### Example Question #31 : How To Simplify An Expression

The product of two consecutive odd negative integers is . What is the smaller of the two integers?

**Possible Answers:**

**Correct answer:**

The problem gives us the product of two consecutive odd negative integers, so we know that one number is less than the other one. Thus, we can set our two numbers as and .

At this point, the more algebraically inclined student might recognize that if , then the equation can be remade to say , and use the quadratic formula to solve.

But this is the ACT, and the faster method by far is to simply recognize that if the product of our two integers is , then must be evenly divisible by our two integers. The only two choices we have that divide evenly into are and , making the smaller number and our answer.

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