Question

What is the solution of the inequality | 3 x − 2 | − 10 ≤ − 6 ?

Answer 1

-2/3
`\leq` x
`\leq` 2

Step-by-step explanation:

First isolate the absolute value

|3x - 2|
`\leq` 4

There are two scenarios now

3x - 2
`\leq` 4 OR -(3x - 2)
`\leq` 4

First case:

3x
`\leq` 6

x
`\leq` 2

Second case:

-3x + 2
`\leq` 4

-3x
`\leq` 2

3x
`\geq` -2

x
`\geq` -2/3

So, -2/3
`\leq` x
`\leq` 2

Interval notation: [-2/3, 2]

Answer 2

`\bold{ANSWER:}`



`\bold{SOLUTION:}`

To solve the inequality |3x - 2| - 10 ≤ −6, we can start by adding 10 to both sides of the inequality:

|3x - 21 ≤ 4

Now, we can split this inequality into two separate
cases:

Case 1: 3x-2≥0
In this case, the absolute value becomes 3x - 2, so we have:

3x-2 ≤ 4

Adding 2 to both sides:

3x ≤ 6

Dividing both sides by 3:
x≤2

Case 2: 3x - 2 < 0
In this case, the absolute value becomes -(3x - 2), so we have:

-(3x-2) ≤ 4

Expanding the negative sign:

-3x + 2 ≤ 4

Subtracting 2 from both sides:

-3x ≤ 2


Dividing both sides by -3 (remember to flip the inequality sign when dividing by a negative number): x = -2/3

Combining the solutions from both cases, we have: x ≤ 2 or x = -2/3

Therefore, the solution to the inequality |3x - 21 - 10 ≤-6 is x UUID’s≤ 2 or x = -2/3.