Solved on Jan 23, 2024

Solve the equation $4p + 25 = 6(p - 3) - 3(4 - 3p)$ .

STEP 1

Assumptions
1. We are given the equation $4p + 25 = 6(p - 3) - 3(4 - 3p)$ .
2. We need to solve for the variable $p$ .

STEP 2

First, we will distribute the multiplication over the parentheses on both sides of the equation.
For the left side of the equation, there is no distribution needed as there are no parentheses.
For the right side of the equation, we distribute $6$ into $(p - 3)$ and $-3$ into $(4 - 3p)$ .

STEP 3

Distribute $6$ into $(p - 3)$ :
$6(p - 3) = 6p - 18$

STEP 4

Distribute $-3$ into $(4 - 3p)$ :
$-3(4 - 3p) = -12 + 9p$

STEP 5

Now, rewrite the original equation with the distributed terms:
$4p + 25 = (6p - 18) - (12 - 9p)$

STEP 6

Next, we simplify the right side of the equation by combining like terms. We need to subtract $12$ and add $9p$ to $6p - 18$ :
$6p - 18 - 12 + 9p$

STEP 7

Combine like terms on the right side:
$6p + 9p - 18 - 12 = 15p - 30$

STEP 8

Now, the equation looks like this:
$4p + 25 = 15p - 30$

STEP 9

To isolate the variable $p$ on one side, we will move all terms containing $p$ to one side and the constant terms to the other side.
First, subtract $4p$ from both sides of the equation to move the $p$ terms to the right side:
$4p + 25 - 4p = 15p - 30 - 4p$

STEP 10

Simplify both sides of the equation:
$25 = 11p - 30$

STEP 11

Next, add $30$ to both sides of the equation to move the constant terms to the left side:
$25 + 30 = 11p - 30 + 30$

STEP 12

Simplify both sides of the equation:
$55 = 11p$

STEP 13

Now, divide both sides of the equation by $11$ to solve for $p$ :
$\frac{55}{11} = \frac{11p}{11}$

STEP 14

Simplify both sides of the equation:
$5 = p$
The solution to the equation is $p = 5$ .

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Solve the equation $4p + 25 = 6(p - 3) - 3(4 - 3p)$ .

STEP 1

Assumptions
1. We are given the equation $4p + 25 = 6(p - 3) - 3(4 - 3p)$ .
2. We need to solve for the variable $p$ .

STEP 2

First, we will distribute the multiplication over the parentheses on both sides of the equation.
For the left side of the equation, there is no distribution needed as there are no parentheses.
For the right side of the equation, we distribute $6$ into $(p - 3)$ and $-3$ into $(4 - 3p)$ .

STEP 3

Distribute $6$ into $(p - 3)$ :
$6(p - 3) = 6p - 18$

STEP 4

Distribute $-3$ into $(4 - 3p)$ :
$-3(4 - 3p) = -12 + 9p$

STEP 5

Now, rewrite the original equation with the distributed terms:
$4p + 25 = (6p - 18) - (12 - 9p)$

STEP 6

Next, we simplify the right side of the equation by combining like terms. We need to subtract $12$ and add $9p$ to $6p - 18$ :
$6p - 18 - 12 + 9p$

STEP 7

Combine like terms on the right side:
$6p + 9p - 18 - 12 = 15p - 30$

STEP 8

Now, the equation looks like this:
$4p + 25 = 15p - 30$

STEP 9

To isolate the variable $p$ on one side, we will move all terms containing $p$ to one side and the constant terms to the other side.
First, subtract $4p$ from both sides of the equation to move the $p$ terms to the right side:
$4p + 25 - 4p = 15p - 30 - 4p$

STEP 10

Simplify both sides of the equation:
$25 = 11p - 30$

STEP 11

Next, add $30$ to both sides of the equation to move the constant terms to the left side:
$25 + 30 = 11p - 30 + 30$

STEP 12

Simplify both sides of the equation:
$55 = 11p$

STEP 13

Now, divide both sides of the equation by $11$ to solve for $p$ :
$\frac{55}{11} = \frac{11p}{11}$

STEP 14

Simplify both sides of the equation:
$5 = p$
The solution to the equation is $p = 5$ .

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Solve the equation 4p+25=6(p−3)−3(4−3p)4p + 25 = 6(p - 3) - 3(4 - 3p)4p+25=6(p−3)−3(4−3p).

STEP 1

Assumptions1. We are given the equation 4p+25=6(p−3)−3(4−3p)4p + 25 = 6(p - 3) - 3(4 - 3p)4p+25=6(p−3)−3(4−3p).2. We need to solve for the variable ppp.

STEP 2

STEP 3

Distribute 666 into (p−3)(p - 3)(p−3):6(p−3)=6p−186(p - 3) = 6p - 186(p−3)=6p−18

STEP 4

Distribute −3-3−3 into (4−3p)(4 - 3p)(4−3p):−3(4−3p)=−12+9p-3(4 - 3p) = -12 + 9p−3(4−3p)=−12+9p

STEP 5

Now, rewrite the original equation with the distributed terms:4p+25=(6p−18)−(12−9p)4p + 25 = (6p - 18) - (12 - 9p)4p+25=(6p−18)−(12−9p)

STEP 6

Next, we simplify the right side of the equation by combining like terms. We need to subtract 121212 and add 9p9p9p to 6p−186p - 186p−18:6p−18−12+9p6p - 18 - 12 + 9p6p−18−12+9p

STEP 7

Combine like terms on the right side:6p+9p−18−12=15p−306p + 9p - 18 - 12 = 15p - 306p+9p−18−12=15p−30

STEP 8

Now, the equation looks like this:4p+25=15p−304p + 25 = 15p - 304p+25=15p−30

STEP 9

STEP 10

Simplify both sides of the equation:25=11p−3025 = 11p - 3025=11p−30

STEP 11

Next, add 303030 to both sides of the equation to move the constant terms to the left side:25+30=11p−30+3025 + 30 = 11p - 30 + 3025+30=11p−30+30

STEP 12

Simplify both sides of the equation:55=11p55 = 11p55=11p

STEP 13

Now, divide both sides of the equation by 111111 to solve for ppp:5511=11p11\frac{55}{11} = \frac{11p}{11}1155​=1111p​

STEP 14

Simplify both sides of the equation:5=p5 = p5=pThe solution to the equation is p=5p = 5p=5.

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Solve the equation $4p + 25 = 6(p - 3) - 3(4 - 3p)$ .

Assumptions
1. We are given the equation $4p + 25 = 6(p - 3) - 3(4 - 3p)$ .
2. We need to solve for the variable $p$ .

Distribute $6$ into $(p - 3)$ :
$6(p - 3) = 6p - 18$

Distribute $-3$ into $(4 - 3p)$ :
$-3(4 - 3p) = -12 + 9p$

Now, rewrite the original equation with the distributed terms:
$4p + 25 = (6p - 18) - (12 - 9p)$

Next, we simplify the right side of the equation by combining like terms. We need to subtract $12$ and add $9p$ to $6p - 18$ :
$6p - 18 - 12 + 9p$

Combine like terms on the right side:
$6p + 9p - 18 - 12 = 15p - 30$

Now, the equation looks like this:
$4p + 25 = 15p - 30$

Simplify both sides of the equation:
$25 = 11p - 30$

Next, add $30$ to both sides of the equation to move the constant terms to the left side:
$25 + 30 = 11p - 30 + 30$

Simplify both sides of the equation:
$55 = 11p$

Now, divide both sides of the equation by $11$ to solve for $p$ :
$\frac{55}{11} = \frac{11p}{11}$

Simplify both sides of the equation:
$5 = p$
The solution to the equation is $p = 5$ .