To solve the equation [tex]\( 5p = -35 \)[/tex] and determine the correct steps to do so, let's go through the algebraic process step-by-step.
1. Start with the given equation:
[tex]\[
5p = -35
\][/tex]
2. To solve for [tex]\( p \)[/tex], you need to isolate [tex]\( p \)[/tex] on one side of the equation. The current coefficient of [tex]\( p \)[/tex] is 5. To isolate [tex]\( p \)[/tex], you need to divide both sides of the equation by 5:
[tex]\[
\frac{5p}{5} = \frac{-35}{5}
\][/tex]
3. Simplify both sides:
[tex]\[
p = -7
\][/tex]
So the solution to the equation [tex]\( 5p = -35 \)[/tex] is [tex]\( p = -7 \)[/tex].
In terms of the given choices:
- "Divide both sides of the equation by -5 to get [tex]\( p = 7 \)[/tex]": This is incorrect because dividing by -5 would not isolate [tex]\( p \)[/tex] correctly or give the right result.
- "Divide both sides of the equation by 5 to get [tex]\( p = 7 \)[/tex]": This is also incorrect because although the division by 5 is correct, the resulting value should be [tex]\( -7 \)[/tex], not [tex]\( 7 \)[/tex].
- "Divide both sides of the equation by 5 to get [tex]\( p = -7 \)[/tex]": This is correct. Dividing both sides by 5 isolates [tex]\( p \)[/tex] and gives the correct solution [tex]\( p = -7 \)[/tex].
- "Divide both sides of the equation by -5 to get [tex]\( p = -7 \)[/tex]": This is incorrect because dividing by -5 would not correctly isolate [tex]\( p \)[/tex] and would not yield the correct solution.
Therefore, the algebraic step that will solve the equation [tex]\( 5p = -35 \)[/tex] correctly is:
Divide both sides of the equation by 5 to get [tex]\( p = -7 \)[/tex].
So the correct choice is:
"Divide both sides of the equation by 5 to get [tex]\( p = -7 \)[/tex]."
