Question

Solve each of the following equations. Show its solution set on a number line.

1) |3x-1|=4
2) 3|2-x|=-6

Pls answer quickly

Answer 1

1) |3x-1|=4

We need to solve two separate equations:

3x - 1 = 4 or 3x - 1 = -4

Solving for x in each equation, we get:

3x = 5 or 3x = -3

x = 5/3 or x = -1

So the solution set is {-1, 5/3} and it can be represented on a number line as:

```

<===o----o===(+)===o---->

-2 -1 5/3 2

```

2) 3|2-x|=-6

We first need to isolate the absolute value expression by dividing both sides by 3:

|2 - x| = -2

The absolute value of any number is always non-negative, so it can never be equal to a negative number, including -2. Therefore, the equation has no solution.

We can represent this on a number line as an empty set:

```

<===o====o====o====>

-2 -1 2

Ø

```