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
To simplify the expression 6(3x−5)+2(3x−5)−8(2x−5), we can distribute the numbers outside the parentheses.
First, distribute 6 to each term inside the first set of parentheses:
6 * 3x = 18x
6 * -5 = -30
So, 6(3x − 5) becomes 18x − 30.
Next, distribute 2 to each term inside the second set of parentheses:
2 * 3x = 6x
2 * -5 = -10
So, 2(3x − 5) becomes 6x − 10.
Finally, distribute -8 to each term inside the third set of parentheses:
-8 * 2x = -16x
-8 * -5 = 40
So, -8(2x − 5) becomes -16x + 40.
Now, substitute the simplified expressions back into the original expression:
(18x - 30) + (6x - 10) - (-16x + 40)
Notice how the subtraction of -16x becomes addition of 16x:
18x - 30 + 6x - 10 + 16x - 40
Combine like terms:
18x + 6x + 16x - 30 - 10 - 40
Combine the numbers:
(18x + 6x + 16x) + (-30 - 10 - 40)
40x + (-80)
Simplify the expression:
40x - 80
So, the simplified expression is 40x − 80.