Answer :

To solve the equation [tex]\(-x = -6\)[/tex] for [tex]\(x\)[/tex], we will follow these steps:

1. Understand the equation: The given equation is [tex]\(-x = -6\)[/tex]. The objective is to isolate [tex]\(x\)[/tex] and find its value.

2. Eliminate the negative sign: To eliminate the negative sign in front of [tex]\(x\)[/tex], we can multiply both sides of the equation by [tex]\(-1\)[/tex]. This technique helps us to "flip" the signs on both sides.

Equation before multiplying:
[tex]\[ -x = -6 \][/tex]

Multiply both sides by [tex]\(-1\)[/tex]:
[tex]\[ (-1) \cdot (-x) = (-1) \cdot (-6) \][/tex]

3. Simplify both sides: When we multiply [tex]\(-x\)[/tex] by [tex]\(-1\)[/tex], the negative signs cancel each other out, and we are left with [tex]\(x\)[/tex]. Similarly, multiplying [tex]\(-6\)[/tex] by [tex]\(-1\)[/tex] converts [tex]\(-6\)[/tex] to [tex]\(6\)[/tex].

[tex]\[ x = 6 \][/tex]

4. Verify the solution: It’s always a good practice to verify the solution by substituting the value back into the original equation to ensure it satisfies the equation.

Substitute [tex]\(x = 6\)[/tex] back into the original equation:
[tex]\[ -6 = -6 \][/tex]

The left-hand side equals the right-hand side, confirming that our solution is correct.

Thus, the solution to the equation [tex]\(-x = -6\)[/tex] is:
[tex]\[ x = 6 \][/tex]