Let's solve the equation [tex]\(\frac{2}{3} x = \frac{3}{8} x + \frac{2}{12}\)[/tex] step-by-step.
### Step 1: Isolate [tex]\( x \)[/tex] on one side of the equation
We start by getting all terms involving [tex]\( x \)[/tex] on the left side of the equation, and constant terms on the right. To do this, we can subtract [tex]\(\frac{3}{8} x\)[/tex] from both sides:
[tex]\[ \frac{2}{3} x - \frac{3}{8} x = \frac{2}{12} \][/tex]
### Step 2: Find a common denominator
To simplify [tex]\(\frac{2}{3} x - \frac{3}{8} x\)[/tex], we find a common denominator for the fractions [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{3}{8}\)[/tex].
The least common multiple (LCM) of 3 and 8 is 24. Therefore, we rewrite the fractions with a denominator of 24:
[tex]\[ \frac{2}{3} = \frac{2 \times 8}{3 \times 8} = \frac{16}{24} \][/tex]
[tex]\[ \frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24} \][/tex]
So, the original equation now looks like:
[tex]\[ \frac{16}{24} x - \frac{9}{24} x = \frac{2}{12} \][/tex]
### Step 3: Simplify the equation
Subtract the fractions on the left side:
[tex]\[ \frac{16 - 9}{24} x = \frac{2}{12} \][/tex]
[tex]\[ \frac{7}{24} x = \frac{2}{12} \][/tex]
### Step 4: Simplify the right side of the equation
We can simplify [tex]\(\frac{2}{12}\)[/tex]:
[tex]\[ \frac{2}{12} = \frac{1}{6} \][/tex]
So, the equation is:
[tex]\[ \frac{7}{24} x = \frac{1}{6} \][/tex]
### Step 5: Solve for [tex]\( x \)[/tex]
To solve for [tex]\( x \)[/tex], multiply both sides by the reciprocal of [tex]\(\frac{7}{24}\)[/tex]:
[tex]\[ x = \frac{1}{6} \times \frac{24}{7} = \frac{24}{42} = \frac{4}{7} \][/tex]
### Final Answer
[tex]\[ x = \frac{4}{7} \][/tex]
Thus, the solution to the equation [tex]\(\frac{2}{3} x = \frac{3}{8} x + \frac{2}{12}\)[/tex] is:
[tex]\[ x = \frac{4}{7} \][/tex]
Approximately, this is [tex]\( x \approx 0.571428571428571 \)[/tex].
