Solved on Jan 11, 2024

Find the value of $r$ given the system of linear equations $-4(r+2) = -12$ and $r+2 = 3$ .

STEP 1

Assumptions
1. We are given a two-step linear equation in the form of $-4(r+2) = -12$ .
2. We need to solve for $r$ .

STEP 2

First, we need to simplify the equation by distributing the multiplication across the parentheses.
$-4(r+2) = -12$

STEP 3

Apply the distributive property to multiply $-4$ by both $r$ and $+2$ .
$-4 \cdot r + (-4) \cdot 2 = -12$

STEP 4

Perform the multiplication.
$-4r - 8 = -12$

STEP 5

Now, we need to isolate the variable $r$ on one side of the equation. We can start by adding $8$ to both sides of the equation to cancel out the $-8$ on the left side.
$-4r - 8 + 8 = -12 + 8$

STEP 6

Simplify both sides of the equation.
$-4r = -4$

STEP 7

Next, we divide both sides of the equation by $-4$ to solve for $r$ .
$\frac{-4r}{-4} = \frac{-4}{-4}$

STEP 8

Simplify the equation by performing the division.
$r = 1$
The solution to the equation is $r = 1$ .

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Find the value of $r$ given the system of linear equations $-4(r+2) = -12$ and $r+2 = 3$ .

STEP 1

Assumptions
1. We are given a two-step linear equation in the form of $-4(r+2) = -12$ .
2. We need to solve for $r$ .

STEP 2

First, we need to simplify the equation by distributing the multiplication across the parentheses.
$-4(r+2) = -12$

STEP 3

Apply the distributive property to multiply $-4$ by both $r$ and $+2$ .
$-4 \cdot r + (-4) \cdot 2 = -12$

STEP 4

Perform the multiplication.
$-4r - 8 = -12$

STEP 5

Now, we need to isolate the variable $r$ on one side of the equation. We can start by adding $8$ to both sides of the equation to cancel out the $-8$ on the left side.
$-4r - 8 + 8 = -12 + 8$

STEP 6

Simplify both sides of the equation.
$-4r = -4$

STEP 7

Next, we divide both sides of the equation by $-4$ to solve for $r$ .
$\frac{-4r}{-4} = \frac{-4}{-4}$

STEP 8

Simplify the equation by performing the division.
$r = 1$
The solution to the equation is $r = 1$ .

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Find the value of rrr given the system of linear equations −4(r+2)=−12-4(r+2) = -12−4(r+2)=−12 and r+2=3r+2 = 3r+2=3.

STEP 1

Assumptions1. We are given a two-step linear equation in the form of −4(r+2)=−12-4(r+2) = -12−4(r+2)=−12.2. We need to solve for rrr.

STEP 2

First, we need to simplify the equation by distributing the multiplication across the parentheses.−4(r+2)=−12-4(r+2) = -12−4(r+2)=−12

STEP 3

Apply the distributive property to multiply −4-4−4 by both rrr and +2+2+2.−4⋅r+(−4)⋅2=−12-4 \cdot r + (-4) \cdot 2 = -12−4⋅r+(−4)⋅2=−12

STEP 4

Perform the multiplication.−4r−8=−12-4r - 8 = -12−4r−8=−12

STEP 5

Now, we need to isolate the variable rrr on one side of the equation. We can start by adding 888 to both sides of the equation to cancel out the −8-8−8 on the left side.−4r−8+8=−12+8-4r - 8 + 8 = -12 + 8−4r−8+8=−12+8

STEP 6

Simplify both sides of the equation.−4r=−4-4r = -4−4r=−4

STEP 7

Next, we divide both sides of the equation by −4-4−4 to solve for rrr.−4r−4=−4−4\frac{-4r}{-4} = \frac{-4}{-4}−4−4r​=−4−4​

STEP 8

Simplify the equation by performing the division.r=1r = 1r=1The solution to the equation is r=1r = 1r=1.

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Find the value of $r$ given the system of linear equations $-4(r+2) = -12$ and $r+2 = 3$ .

Assumptions
1. We are given a two-step linear equation in the form of $-4(r+2) = -12$ .
2. We need to solve for $r$ .

First, we need to simplify the equation by distributing the multiplication across the parentheses.
$-4(r+2) = -12$

Apply the distributive property to multiply $-4$ by both $r$ and $+2$ .
$-4 \cdot r + (-4) \cdot 2 = -12$

Perform the multiplication.
$-4r - 8 = -12$

Now, we need to isolate the variable $r$ on one side of the equation. We can start by adding $8$ to both sides of the equation to cancel out the $-8$ on the left side.
$-4r - 8 + 8 = -12 + 8$

Simplify both sides of the equation.
$-4r = -4$

Next, we divide both sides of the equation by $-4$ to solve for $r$ .
$\frac{-4r}{-4} = \frac{-4}{-4}$

Simplify the equation by performing the division.
$r = 1$
The solution to the equation is $r = 1$ .