# How do you solve #2- 3[ x - 2( x + 1) ] = x - [ 2- ( x - 3) ]#?

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To solve the equation (2 - 3[x - 2(x + 1)] = x - [2 - (x - 3)]), follow these steps:

- Distribute and simplify within each set of brackets.
- Combine like terms on each side of the equation.
- Isolate the variable (x) on one side of the equation.
- Solve for (x).

Starting with step 1:

(2 - 3[x - 2(x + 1)] = x - [2 - (x - 3)])

(= 2 - 3[x - 2x - 2] = x - [2 - x + 3])

(= 2 - 3[x - 2x - 2] = x - [5 - x])

(= 2 - 3[x - 2x - 2] = x - 5 + x)

Now, simplify further:

(2 - 3[x - 2x - 2] = 2x - 5)

(= 2 - 3[-x - 2] = 2x - 5)

(= 2 + 3x + 6 = 2x - 5)

Combine like terms:

(3x + 8 = 2x - 5)

Now, isolate the variable (x):

(3x - 2x = -5 - 8)

(x = -13)

So, the solution to the equation is (x = -13).

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To solve the equation (2 - 3[x - 2(x + 1)] = x - [2 - (x - 3)]), follow these steps:

- Simplify the expressions within brackets.
- Apply the distributive property where necessary.
- Combine like terms.
- Solve for the variable (x).

Starting with the given equation:

[2 - 3[x - 2(x + 1)] = x - [2 - (x - 3)]]

[2 - 3[x - 2x - 2] = x - [2 - x + 3]]

[2 - 3[x - 2x - 2] = x - [5 - x]]

Now simplify inside the brackets:

[2 - 3[x - 2x - 2] = x - [5 - x]]

[2 - 3[-x - 2] = x - [5 - x]]

[2 + 3x + 6 = x - (5 - x)]

[8 + 3x = x - 5 + x]

[8 + 3x = 2x - 5]

Now, isolate (x) on one side:

[8 + 3x = 2x - 5]

[3x - 2x = -5 - 8]

[x = -13]

Therefore, the solution to the equation is (x = -13).

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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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