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How do you solve #-5(2b+7)+b< -b-11#?

Answer 1

Abigail Allen

#b > -3#

First, expand the term in parenthesis:

#-10b - 35 + b < -b - 11#

Next, combine like terms:

#-9b - 35 < -b - 11#

Now, isolate the #b# terms on one side of the inequality and the constants on the other side of the inequality while keeping everything balanced:

#-9b - 35 + 35 + b < -b - 11 + 35 + b#

#-9b + b < -11 + 35#

#-8b < 24#

Finally we solve for #b# by dividing each side of the inequality by #-8#. However, remember to "flip" or reverse the inequality because we are dividing by a negative number:

#(-8b)/(-8) > 24/(-8)#

#b > -3#

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Answer 2

Ethan Adkins

To solve the inequality -5(2b+7)+b < -b-11, follow these steps:

Distribute the -5 across the parentheses: -10b - 35 + b < -b - 11
Combine like terms: -9b - 35 < -b - 11
Add b to both sides to isolate terms with b: -9b + b - 35 < -b + b - 11 -8b - 35 < -11
Add 35 to both sides to isolate -8b: -8b - 35 + 35 < -11 + 35 -8b < 24
Divide both sides by -8. Remember to reverse the inequality since you're dividing by a negative number: (-8b) / -8 > 24 / -8 b > -3

So, the solution to the inequality is b > -3.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you solve #-5(2b+7)+b&lt; -b-11#?

How do you solve #-5(2b+7)+b< -b-11#?