QuestionSolve the equation. $3.6 w=2(0.8 w+12)$
Enter the correct answer in the box.
Show Hints $w=$ $\square$

Studdy Solution

STEP 1

1. The equation $3.6w = 2(0.8w + 12)$ is a linear equation in one variable, $w$ .
2. The goal is to find the value of $w$ that satisfies the equation.
3. Basic algebraic operations, such as distribution and combining like terms, will be used.

STEP 2

1. Expand the equation by distributing the constant on the right side.
2. Simplify the equation by combining like terms.
3. Isolate the variable $w$ to solve for it.
4. Verify the solution by substituting it back into the original equation.

STEP 3

Start by distributing the $2$ on the right side of the equation:
$3.6w = 2 \times 0.8w + 2 \times 12$
This gives:
$3.6w = 1.6w + 24$

STEP 4

Next, we need to get all terms involving $w$ on one side of the equation. Subtract $1.6w$ from both sides:
$3.6w - 1.6w = 24$
Simplify the left side:
$2.0w = 24$

STEP 5

Now, solve for $w$ by dividing both sides by $2.0$ :
$w = \frac{24}{2.0}$
Calculate the division:
$w = 12$

STEP 6

Verify the solution by substituting $w = 12$ back into the original equation:
Original equation:
$3.6(12) = 2(0.8(12) + 12)$
Calculate both sides:
Left side:
$3.6 \times 12 = 43.2$
Right side:
$2(0.8 \times 12 + 12) = 2(9.6 + 12) = 2 \times 21.6 = 43.2$
Both sides are equal, confirming the solution is correct.
The solution is:
$\boxed{12}$

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