Question $8-2 k=-3 k-2$

Studdy Solution

STEP 1

1. The equation $8 - 2k = -3k - 2$ is a linear equation with one variable, $k$ .
2. The goal is to find the value of $k$ that satisfies the equation.
3. We will use basic algebraic operations to isolate the variable.

STEP 2

1. Simplify and rearrange the equation to combine like terms.
2. Isolate the variable $k$ on one side of the equation.
3. Solve for $k$ .
4. Check the solution by substituting it back into the original equation.

STEP 3

Start by simplifying and rearranging the equation to get all terms involving $k$ on one side and constant terms on the other side.
Add $3k$ to both sides to move the $k$ terms to one side:
$8 - 2k + 3k = -3k + 3k - 2$
This simplifies to:
$8 + k = -2$

STEP 4

Now, isolate the variable $k$ by moving the constant term to the other side.
Subtract 8 from both sides:
$8 + k - 8 = -2 - 8$
This simplifies to:
$k = -10$

STEP 5

Check the solution by substituting $k = -10$ back into the original equation:
$8 - 2(-10) = -3(-10) - 2$
Simplify both sides:
Left-hand side: $8 + 20 = 28$
Right-hand side: $30 - 2 = 28$
Both sides are equal, confirming the solution is correct.
The solution is:
$\boxed{-10}$

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