Certainly! Let's solve the equation step-by-step.
Given equation:
[tex]\[ \frac{c x + d x}{a} = g \][/tex]
### Step 1: Combine Like Terms in the Numerator
First, notice that in the numerator, [tex]\(c x\)[/tex] and [tex]\(d x\)[/tex] are like terms. We can simplify:
[tex]\[ c x + d x = (c + d)x \][/tex]
### Step 2: Substitute Back into the Equation
Substitute [tex]\((c + d)x\)[/tex] back into the original equation:
[tex]\[ \frac{(c + d)x}{a} = g \][/tex]
### Step 3: Eliminate the Denominator
To isolate [tex]\(x\)[/tex], we want to eliminate the fraction. Multiply both sides of the equation by [tex]\(a\)[/tex]:
[tex]\[ (c + d)x = a g \][/tex]
### Step 4: Solve for [tex]\(x\)[/tex]
Now, solve for [tex]\(x\)[/tex] by dividing both sides of the equation by [tex]\((c + d)\)[/tex]:
[tex]\[ x = \frac{a g}{c + d} \][/tex]
So, the solution for [tex]\(x\)[/tex] is:
[tex]\[ x = \frac{a g}{c + d} \][/tex]
