Expressions - ACT Math

First, we solve each expression by plugging in the given values for x and y:

3(22) – 2(3) = 12 – 6 = 6

3(32) – 2(2) = 27 – 4 = 23

Then we find the difference between the first and second expressions’ values:

23 – 6 = 17

Plug in 3 for x, giving you 36 + 18 – 17, which equals 37.

The whole trip is 60 miles, and it takes 90 minutes, which is 1.5 hours.

Miles per hour is 60/1.5 = 40 mph

–3_w_ = –9 – (xy/2)

w = 3 + (xy/6)

Plug in 7 for x and you get 5(49) + 16(7) + 7 = 364

Substitute the values of a and b into the equation. Then

2a2 + 3ab – 7

(2 x 42 ) + (3 x 4 x 3) – 7

(2 x 16) + (36) -7

32 + 36 – 7

61

First, we can use the property of exponents that xy/xz = xy–z

Then we can use the property of exponents that states x–y = 1/xy

a–1b5c–1 = b5/ac

To answer this question we need to isolate x. A useful first step is to subtract 5 from both sides. The expression then becomes 3x = 2x – 12. Then we can subtract 2x from both sides. This leaves x = –12.

Begin by distributing each part:

2x(x2 + 4ax – 3a2) = 2x * x2 + 2x * 4ax – 2x * 3a2 = 2x3 + 8ax2 – 6a2x

The second:

–4a2(4x + 3a) = –16a2x – 12a3

Now, combine these:

2x3 + 8ax2 – 6a2x – 16a2x – 12a3

The only common terms are those with a2x; therefore, this reduces to

2x3 + 8ax2 – 22a2x – 12a3

This is the same as the given answer:

–12a3 – 22a2x + 8ax2 + 2x3

Since both rational terms in the expression have the common denominator , combine the numerators and simplify like terms:

The easy way to solve this problem is to multiply both halves of the fraction by the conjugate of the denominator, since this will eliminate the radical in the denominator.

Conjugate the fraction.

Next, simplify the denominator, eliminating any terms you can along the way.

Thus, is our answer.

Solve for equation for y – x = 3. Then, plug in 3 into (y – x)3 = 27.

Since both expressions have a common denominator, x2, we can just recopy the denominator and focus on the numerators. We get (9x - 2) - (6x - 8). We must distribute the negative sign over the 6x - 8 expression which gives us 9x - 2 - 6x + 8 ( -2 minus a -8 gives a +6 since a negative and negative make a positive). The numerator is therefore 3x + 6.

Since both fractions in the expression have a common denominator of , we can combine like terms into a single numerator over the denominator:

Since both terms in the expression have the common denominator , combine the fractions and simplify the numerators:

Notice that the denominator are the same for both terms. Since they are both the same, the fractions can be added. The denominator will not change in this problem.

When working with complex fractions, it is important not to let them intimidate you. They follow the same rules as regular fractions!

In this case, our problem is made easier by the fact that we already have a common denominator. Nothing fancy is required to start. Simply add the numerators:

For our next step, we need to combine like terms. This is easier to see if we group them together.

Thus, our final answer is:

In order to add fractions, we must first make sure they have the same denominator.

So, we multiply by and get the following:

Then, we add across the numerators and simplify:

To simplify the following, a common denominator must be achieved. In this case, the first term must be multiplied by (x+2) in both the numerator and denominator and likewise with the second term with (x-3).

Find the least common denominator between x-3 and x-4, which is (x-3)(x-4). Therefore, you have . Multiplying the terms out equals . Combining like terms results in .