# Simplify the following expression: #101-{[(110 -: 2)-: 11]xx(10+4xx2) +7}+ [8xx(20 -: 5-1)-3xx3] -: 5#?

Take your time and methodically go through each bracket and you'll eventually get to

Wow... that's one big equation. Let's take this step by step.

First we'll start with the original:

There are brackets (and brackets within brackets) in this, so I'm going to work those first. There are 2 sets here and I'll work them side by side. In this first step, let's do the division and in the second set we have both addition and multiplication - so we'll do the multiplication first:

I can now do the next division in the first bracket and do the addition in the second:

We'll finish this up with the multiplication first, then the addition:

Let's now work that second bracket:

There's a bracket in here that we need to work first. Within that bracket there is both division and subtraction - we'll divide first:

and now the subtraction:

We now have 2 multiplications and a subtraction, so we'll do the multiplications first:

Let's substitute that into the original:

Almost there! We have subtraction, addition, and division. We'll do the division first:

and now the subtraction and addition:

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Count the number of terms and work through each one carefully. Each term must give a number answer.

There are only 3 terms in this expression:

Now for the third term:

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To simplify the given expression:

- ( \frac{110}{2} = 55 )
- ( 55 ÷ 11 = 5 )
- ( 10 + (4 \times 2) = 10 + 8 = 18 )
- ( 5 \times 2 = 10 )
- ( 20 ÷ (5 - 1) = 20 ÷ 4 = 5 )
- ( 3 \times 3 = 9 )

Now substitute these values back into the expression and simplify step by step:

(101 - \left[ \left( 55 - 5 \right) \times \left( 18 + 7 \right) + 7 \right] + \left[ 8 \times \left( 5 - 3 \times 3 \right) ÷ 5 \right])

(101 - \left[ 50 \times 25 + 7 \right] + \left[ 8 \times (5 - 9) ÷ 5 \right])

(101 - \left[ 1250 + 7 \right] + \left[ 8 \times (-4) ÷ 5 \right])

(101 - 1257 + \left[ -32 ÷ 5 \right])

(101 - 1257 + (-6.4))

(-1156.4)

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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.

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.

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.

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