## Answer :

[tex]\[ 3(x-2) = 22 - x \][/tex]

Let's solve the equation step-by-step:

1.

**Distribute the 3 on the left side**:

[tex]\[ 3 \cdot x - 3 \cdot 2 = 22 - x \][/tex]

Which simplifies to:

[tex]\[ 3x - 6 = 22 - x \][/tex]

2.

**Move all terms involving [tex]\(x\)[/tex] to one side of the equation**:

We add [tex]\(x\)[/tex] to both sides to get the [tex]\(x\)[/tex] terms together:

[tex]\[ 3x + x - 6 = 22 \][/tex]

This simplifies to:

[tex]\[ 4x - 6 = 22 \][/tex]

3.

**Isolate the [tex]\(x\)[/tex] term**:

Add 6 to both sides to move the constant to the right side:

[tex]\[ 4x - 6 + 6 = 22 + 6 \][/tex]

This simplifies to:

[tex]\[ 4x = 28 \][/tex]

4.

**Solve for [tex]\(x\)[/tex]**:

Divide by 4:

[tex]\[ \frac{4x}{4} = \frac{28}{4} \][/tex]

This simplifies to:

[tex]\[ x = 7 \][/tex]

After all these steps, we have found [tex]\(x = 7\)[/tex].

Conclusively, the equation [tex]\(3(x-2)=22-x\)[/tex] has a single unique solution. Therefore, the number of solutions is:

**One**