Certainly! Let's solve the equation [tex]\(5x + 15 = 0\)[/tex] and justify each step with appropriate properties or explanations.
1. Original Equation:
[tex]\[
5x + 15 = 0
\][/tex]
This is the given equation that we need to solve for [tex]\(x\)[/tex].
2. Subtract 15 from both sides:
[tex]\[
5x + 15 - 15 = 0 - 15
\][/tex]
Explanation:
We apply the Subtraction Property of Equality, which states that if you subtract the same number from both sides of an equation, the two sides remain equal.
3. Simplify:
[tex]\[
5x = -15
\][/tex]
Explanation:
On the left side, [tex]\(15 - 15\)[/tex] simplifies to [tex]\(0\)[/tex]. So, we have [tex]\(5x = -15\)[/tex].
4. Divide both sides by 5:
[tex]\[
\frac{5x}{5} = \frac{-15}{5}
\][/tex]
Explanation:
We apply the Division Property of Equality, which states that if you divide both sides of an equation by the same non-zero number, the two sides remain equal.
5. Simplify:
[tex]\[
x = -3
\][/tex]
Explanation:
On the left side, [tex]\( \frac{5x}{5} \)[/tex] simplifies to [tex]\( x \)[/tex] because [tex]\(5/5 = 1\)[/tex]. On the right side, [tex]\( \frac{-15}{5} \)[/tex] simplifies to [tex]\(-3\)[/tex].
So, the solution to the equation [tex]\(5x + 15 = 0\)[/tex] is:
[tex]\[
x = -3
\][/tex]
