Question $12 r-18=13 r+18$

Studdy Solution

STEP 1

1. The equation $12r - 18 = 13r + 18$ is a linear equation in one variable.
2. The goal is to find the value of $r$ that satisfies the equation.
3. Basic algebraic operations such as addition, subtraction, and division will be used.

STEP 2

1. Simplify the equation by moving all terms involving $r$ to one side.
2. Move constant terms to the opposite side.
3. Solve for $r$ .
4. Check the solution by substituting it back into the original equation.

STEP 3

Start by moving all terms involving $r$ to one side. Subtract $12r$ from both sides:
$12r - 18 - 12r = 13r + 18 - 12r$
Simplify:
$-18 = r + 18$

STEP 4

Move the constant term on the right side to the left side by subtracting 18 from both sides:
$-18 - 18 = r + 18 - 18$
Simplify:
$-36 = r$

STEP 5

The solution for $r$ is:
$r = -36$

STEP 6

Check the solution by substituting $r = -36$ back into the original equation:
Original equation: $12r - 18 = 13r + 18$
Substitute $r = -36$ :
$12(-36) - 18 = 13(-36) + 18$
Calculate both sides:
Left side: $12(-36) - 18 = -432 - 18 = -450$
Right side: $13(-36) + 18 = -468 + 18 = -450$
Both sides are equal, confirming the solution is correct.
The solution is:
$\boxed{-36}$

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