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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.

3 answers

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.

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.

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.