Simplify the expression.
the quantity negative 1 over 8 times r minus 5 minus 1 over 6 times r end quantity minus the quantity negative 6 over 8 times r plus 3 end quantity
To simplify the expression, let's break it down into smaller parts and then combine them:
-1/8 * r - 5 - 1/6 * r - (-6/8 * r + 3)
First, let's simplify the multiplication:
(-r/8) - 5 - (r/6) - (-3r/4 + 3)
Next, let's combine like terms:
(-r/8 - r/6) -5 -(-3r/4 + 3)
To combine the fractions, we need a common denominator. The least common multiple of 8 and 6 is 24, so we can rewrite the expression as follows:
(-3r/24 - 4r/24) -5 -(-18r/24 + 3)
Combine the fractions:
(-7r/24) -5 + (18r/24) - 3
(-7r -120r)/24 + (-5 - 3)
(-127r)/24 - 8
So, the simplified expression is (-127r)/24 - 8.