QuestionSolve the equation: $\frac{3}{4}(x+6)=-\frac{1}{4} x$ . What is the solution?

Studdy Solution

STEP 1

Assumptions1. We are given the equation $\frac{3}{4}(x+6)=-\frac{1}{4} x$ . We are tasked with finding the value of $x$ that satisfies this equation.

STEP 2

First, we need to distribute the $\frac{}{4}$ on the left side of the equation.
$\frac{}{4}x + \frac{}{4} \cdot6 = -\frac{1}{4}x$

STEP 3

Now, simplify the multiplication on the left side of the equation.
$\frac{3}{}x + \frac{18}{} = -\frac{1}{}x$

STEP 4

Further simplify the left side of the equation.
$\frac{3}{4}x + \frac{9}{2} = -\frac{1}{4}x$

STEP 5

Next, we want to get all terms involving $x$ on one side of the equation and constants on the other side. Let's add $\frac{1}{4}x$ to both sides of the equation.
$\frac{3}{4}x + \frac{1}{4}x + \frac{9}{2} =0$

STEP 6

implify the left side of the equation.
$x + \frac{9}{2} =0$

STEP 7

Finally, we solve for $x$ by subtracting $\frac{9}{2}$ from both sides of the equation.
$x = -\frac{9}{2}$ So, the solution to the equation $\frac{3}{4}(x+6)=-\frac{1}{4} x$ is $x = -\frac{9}{2}$ .

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