Question Solve the equation $-13=-4.6(14-2p)$ , and round the answer to the nearest hundredth.

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $-13=-4.6(14-2p)$ .
2. We need to solve for the variable $p$ .
3. The final answer should be rounded to the nearest hundredth.

STEP 2

First, we will distribute the $-4.6$ across the terms inside the parentheses.
$-13 = -4.6 \times 14 + 4.6 \times 2p$

STEP 3

Perform the multiplication to simplify the equation.
$-13 = -64.4 + 9.2p$

STEP 4

Next, we will isolate the term with the variable $p$ on one side of the equation by adding $64.4$ to both sides.
$-13 + 64.4 = -64.4 + 64.4 + 9.2p$

STEP 5

Simplify both sides of the equation.
$51.4 = 9.2p$

STEP 6

Now, divide both sides of the equation by $9.2$ to solve for $p$ .
$\frac{51.4}{9.2} = \frac{9.2p}{9.2}$

STEP 7

Perform the division to find the value of $p$ .
$p = \frac{51.4}{9.2}$

STEP 8

Calculate the value of $p$ .
$p = 5.58695652...$

STEP 9

Round the answer to the nearest hundredth, as per the problem's instructions.
$p \approx 5.59$
The solution to the equation is $p \approx 5.59$ .

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