# How do you solve #3|2x + -5| + 3 = 42#?

Dividing both sides by 3

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Solve:

Make the absolute value simpler.

Simplify.

Simplify.

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First, solve the following equation:

Simplify.

Simplify.

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Complete the second equation:

Expand.

Simplify.

Simplify.

ด ฟฟ ฟฟ

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To solve the equation (3|2x - 5| + 3 = 42), follow these steps:

- Subtract 3 from both sides of the equation to isolate the absolute value term.

[3|2x - 5| = 39]

- Divide both sides of the equation by 3 to isolate the absolute value term.

[|2x - 5| = \frac{39}{3}]

[|2x - 5| = 13]

- Now, you have two cases to consider for the absolute value:

a) (2x - 5 = 13)

b) (2x - 5 = -13)

- Solve each case separately:

a) For (2x - 5 = 13):

[2x = 13 + 5] [2x = 18] [x = \frac{18}{2}] [x = 9]

b) For (2x - 5 = -13):

[2x = -13 + 5] [2x = -8] [x = \frac{-8}{2}] [x = -4]

- Therefore, the solutions to the equation (3|2x - 5| + 3 = 42) are (x = 9) and (x = -4).

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To solve the equation (3|2x - 5| + 3 = 42), follow these steps:

- Subtract 3 from both sides to isolate the absolute value term.
- Divide both sides by 3.
- Solve for (|2x - 5|) by isolating it on one side of the equation.
- Once you have (|2x - 5|) isolated, set up two equations: one positive and one negative, equating the expression within the absolute value bars to both positive and negative values.
- Solve each equation separately.
- Check the solutions obtained by plugging them back into the original equation to ensure they are valid.

The solutions will depend on the specific values of (x) that satisfy the conditions of the equations formed in step 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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