Simplify the expression: 6(3x−5)+2(3x−5)−8(3x−5)

Question

(1 point)
Responses

35x−60
35 x minus 60

24x−40
24 x minus 40

48x−80
48 x minus 80

0
0

Answer 1

To simplify the expression \(6(3x−5)+2(3x−5)−8(3x−5)\), we can combine like terms.

First, notice that \( (3x - 5) \) is a common factor in all the terms:

\[ 6(3x - 5) + 2(3x - 5) - 8(3x - 5) \]

We can factor out \( (3x - 5) \):

\[ (3x - 5)(6 + 2 - 8) \]

Now simplify the expression inside the parentheses:

\[ 6 + 2 - 8 = 8 - 8 = 0 \]

So, now we have:

\[ (3x - 5)(0) = 0 \]

Thus, the simplified expression is:

\[ \boxed{0} \]

Answer 2

Evaluate the expression −4x+7y
when x=−2
and y=−4
.(1 point)
Responses

−20
negative 20

20
20

−36
negative 36

36

Answer 3

To evaluate the expression \(-4x + 7y\) when \(x = -2\) and \(y = -4\), we can substitute these values into the expression:

\[ -4(-2) + 7(-4) \]

Now calculate each term:

1. \(-4(-2) = 8\)
2. \(7(-4) = -28\)

Now, substitute these values back into the expression:

\[ 8 - 28 \]

Now, perform the subtraction:

\[ 8 - 28 = -20 \]

Thus, the final result is:

\[ \boxed{-20} \]

Answer 4

Simplify 4x+6(3x−2)
(1 point)
Responses

22x−12
22 x minus 12

22x−2
22 x minus 2

10x−12
10 x minus 12

18x−2

Answer 5

To simplify the expression \(4x + 6(3x - 2)\), we first distribute the \(6\) in the second term:

1. Distribute \(6\) across \(3x - 2\): \[ 6(3x) - 6(2) = 18x - 12 \]

Now we can rewrite the expression:

\[ 4x + 18x - 12 \]

Next, combine the like terms (\(4x\) and \(18x\)):

\[ (4x + 18x) - 12 = 22x - 12 \]

So, the simplified expression is:

\[ \boxed{22x - 12} \]

Answer 6

Simplify 1/3(9x − 5)
(1 point)
Responses

6x−5
6 x minus 5

3x−5/3
3 x minus 5 thirds

3x−5
3 x minus 5

6x−2

Answer 7

To simplify the expression \(\frac{1}{3}(9x - 5)\), we distribute \(\frac{1}{3}\) to both terms inside the parentheses:

1. For \(9x\): \[ \frac{1}{3} \cdot 9x = 3x \]

2. For \(-5\): \[ \frac{1}{3} \cdot (-5) = -\frac{5}{3} \]

Now, putting it all together, we have:

\[ 3x - \frac{5}{3} \]

So, the simplified expression is:

\[ \boxed{3x - \frac{5}{3}} \]

Answer 8

Which factorization is equivalent to this expression?

30x+70


(1 point)
Responses

7(3x+10)
7 times open paren 3 x plus 10 close paren

10(x+7)
10 times open paren x plus 7 close paren

30(x+2)
30 times open paren x plus 2 close paren

10(3x+7)

Answer 9

To factor the expression \(30x + 70\), we first need to find the greatest common factor (GCF) of the two terms, which is \(10\).

Now we can factor \(10\) out of the expression:

\[ 30x + 70 = 10(3x) + 10(7) = 10(3x + 7) \]

So, the factorization of \(30x + 70\) is:

\[ \boxed{10(3x + 7)} \]

Answer 10

Which factorization is equivalent to this expression? 81x−36
(1 point)
Responses

9x−4
9 x minus 4

−9(9x−4)
negative 9 times open paren 9 x minus 4 close paren

9(9x−8)
9 times open paren 9 x minus 8 close paren

9(9x−4)

Answer 11

To factor the expression \(81x - 36\), we first identify the greatest common factor (GCF) of the two terms.

The GCF of \(81\) and \(36\) is \(9\). Now we can factor \(9\) out of the expression:

\[ 81x - 36 = 9(9x) - 9(4) = 9(9x - 4) \]

Thus, the factorization of \(81x - 36\) is:

\[ \boxed{9(9x - 4)} \]