Question

Simplify the expression.

6(3x−5)+2(3x−5)−8(2x−5)

(1 point)
Responses

8x
8 x

24x−40
24 x minus 40

36x−60
36 x minus 60

48x−80.

Answer 1

Determine the unknown number.

Twice a number, increased by 3 is 7.

(1 point)
Responses

The number is 2.
The number is 2.

The number is 8.
The number is 8.

The number is 20.
The number is 20.

The number is 5.

Answer 2

To simplify the expression \( 6(3x - 5) + 2(3x - 5) - 8(2x - 5) \), we can start by distributing the constants across the expressions in the parentheses:

1. Distribute \(6\) and \(2\) in the first two terms:
\[
6(3x - 5) = 18x - 30
\]
\[
2(3x - 5) = 6x - 10
\]

2. Now distribute \(-8\) in the third term:
\[
-8(2x - 5) = -16x + 40
\]

3. Now we can combine all the terms:
\[
(18x - 30) + (6x - 10) + (-16x + 40)
\]

4. Combine like terms (combine the \(x\) terms and the constant terms):
- For the \(x\) terms:
\[
18x + 6x - 16x = 8x
\]
- For the constant terms:
\[
-30 - 10 + 40 = 0
\]

5. Putting it all together:
\[
8x + 0 = 8x
\]

So, the simplified expression is \(8x\).

The correct answer is **8x**.

Answer 3

Let's denote the unknown number as \( x \).

According to the problem, twice the number increased by 3 equals 7. We can write this as an equation:

\[
2x + 3 = 7
\]

Now, we can solve for \( x \):

1. Subtract 3 from both sides:
\[
2x = 7 - 3
\]
\[
2x = 4
\]

2. Now divide both sides by 2:
\[
x = \frac{4}{2}
\]
\[
x = 2
\]

So the unknown number is **2**.

The correct response is **The number is 2.**