Simplify −3/4r + 3 − 5/6r − 6 .(1 point)
To simplify the given expression, we can combine like terms:
−(3/4r) + 3 − (5/6r) − 6
First, let's combine the terms with "r":
-3/4r - 5/6r
To combine these terms, we need to find a common denominator for 4 and 6, which is 12. Then, we can rewrite the terms with this denominator:
-9/12r - 10/12r
Now, we can combine these terms:
-9/12r - 10/12r = -19/12r
Therefore, the simplified expression is:
-19/12r + 3 - 6
Finally, we can combine the remaining terms:
-19/12r + 3 - 6 = -19/12r - 3
So, the simplified expression is -19/12r - 3.
Expand 8(3p + 2) .(1 point)
To expand the given expression, we can distribute the 8 to each term inside the parentheses:
8(3p + 2) = 8(3p) + 8(2)
Now, we can simplify each term:
8(3p) = 24p
8(2) = 16
Therefore, the expanded expression is:
24p + 16.
Expand −4(6a − 5) .(1 point)
To expand the given expression, we can distribute the -4 to each term inside the parentheses:
-4(6a - 5) = -4(6a) - 4(-5)
Now, we can simplify each term:
-4(6a) = -24a
-4(-5) = 20
Therefore, the expanded expression is:
-24a + 20.
Expand 7/4(8h+3) .(1 point)
To expand the given expression, we can distribute the 7/4 to each term inside the parentheses:
(7/4)(8h + 3) = (7/4)(8h) + (7/4)(3)
Now, let's simplify each term:
(7/4)(8h) = 56h/4 = 14h
(7/4)(3) = 21/4
Therefore, the expanded expression is:
14h + 21/4 or 14h + 5.25
Expand −5/6(9b−12) .(1 point)
To expand the given expression, we can distribute the -5/6 to each term inside the parentheses:
(-5/6)(9b - 12) = (-5/6)(9b) - (-5/6)(12)
Now, let's simplify each term:
(-5/6)(9b) = -45b/6 = -15b/2
(-5/6)(12) = -60/6 = -10
Therefore, the expanded expression is:
-15b/2 - 10.