Certainly! Let's solve the equation step-by-step.
Given equation:
[tex]\[ 0.08x + 0.15(6) = 0.10(x + 6) \][/tex]
First, simplify both sides of the equation:
1. Distribute the constants:
[tex]\[ 0.08x + 0.15 \cdot 6 = 0.10(x + 6) \][/tex]
[tex]\[ 0.08x + 0.90 = 0.10x + 0.60 \][/tex]
Next, we move all terms involving [tex]\( x \)[/tex] to one side and constant terms to the other side:
2. Subtract [tex]\( 0.10x \)[/tex] from both sides:
[tex]\[ 0.08x - 0.10x + 0.90 = 0.60 \][/tex]
[tex]\[ -0.02x + 0.90 = 0.60 \][/tex]
3. Subtract 0.90 from both sides to isolate the variable term on one side:
[tex]\[ -0.02x = 0.60 - 0.90 \][/tex]
[tex]\[ -0.02x = -0.30 \][/tex]
Finally, solve for [tex]\( x \)[/tex] by dividing both sides by [tex]\(-0.02\)[/tex]:
4. Divide both sides by [tex]\(-0.02\)[/tex]:
[tex]\[ x = \frac{-0.30}{-0.02} \][/tex]
[tex]\[ x = 15.0 \][/tex]
Thus, the solution to the equation is:
[tex]\[ x = 15.0 \][/tex]
