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]
