QuestionSolve for $p$ in the equation: $-15 p - 4(6 - 6 p) = 6(p - 3) - 3$ . What is the solution set? A, B, or C?

Studdy Solution

STEP 1

Assumptions1. We are solving for the variable $p$ in the equation $-15p -4(6 -6p) =6(p -3) -3$ . . The equation is a linear equation, and we assume that it has a solution.
3. The solution set is either a single real number, all real numbers (in case the equation is an identity), or no solution (in case the equation is a contradiction).

STEP 2

First, we need to simplify the equation by distributing the numbers outside the parentheses on both sides of the equation.
On the left side, distribute $-4$ across $(6 -6p)$ , and on the right side, distribute $6$ across $(p -)$ .
$-15p -4 \cdot6 +4 \cdot6p =6 \cdot p -6 \cdot -$

STEP 3

implify the equation by performing the multiplication.
$-15p -24 +24p =6p -18 -3$

STEP 4

Combine like terms on both sides of the equation.
$9p -24 =6p -21$

STEP 5

To isolate $p$ , we need to get all terms with $p$ on one side of the equation and the constants on the other side. Subtract $p$ from both sides to get the $p$ terms on the left side and add $24$ to both sides to get the constants on the right side.
$9p -p =21 +24$

STEP 6

implify the equation by performing the subtraction and addition.
$3p =45$

STEP 7

Finally, to solve for $p$ , divide both sides of the equation by $3$ .
$p = \frac{45}{3}$

STEP 8

implify the right side of the equation to find the value of $p$ .
$p =15$

STEP 9

Now that we have the value of $p$ , we need to check our solution by substituting $p =15$ back into the original equation.
$-15(15) -4(6 -6(15)) =6(15 -3) -3$

STEP 10

implify the equation by performing the multiplication.
$-225 -4(-84) =72 -3$

STEP 11

Perform the multiplication and subtraction to check if both sides of the equation are equal.
$-225 +336 =69$

STEP 12

implify both sides of the equation.
$111 =69$

STEP 13

Since $111 \neq69$ , our solution $p =15$ is incorrect. Therefore, the equation has no solution.
The solution set is $\varnothing$ , so the equation is a contradiction.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms