QuestionSolve for $p$ : $-160=22+8(3p-4)$ . Enter your answer as a decimal. $p=$

Studdy Solution

STEP 1

Assumptions1. We are solving for $p$ in the equation $-160=22+8(3p-4)$ . The operations follow the order of operations, PEMAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction)

STEP 2

First, we need to simplify the equation. We can start by distributing the8 inside the parentheses.
$-160 =22 +8 \cdotp -8 \cdot4$

STEP 3

Now, simplify the multiplication.
$-160 =22 +24p -32$

STEP 4

Next, we combine like terms on the right side of the equation.
$-160 =24p -10$

STEP 5

We want to isolate $p$ on one side of the equation. We can do this by adding10 to both sides of the equation.
$-160 +10 =24p -10 +10$

STEP 6

implify both sides of the equation.
$-150 =24p$

STEP 7

Finally, to solve for $p$ , we divide both sides of the equation by24.
$p = \frac{-150}{24}$

STEP 8

implify the right side of the equation to find the value of $p$ .
$p = -6.25$ So, the solution to the equation is $p = -6.25$ .

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