To solve the equation [tex]\( 3x + \frac{9}{7} = \frac{3}{7} \)[/tex] for the variable [tex]\( x \)[/tex], follow these steps:
1. Isolate the term with [tex]\( x \)[/tex]:
[tex]\[
3x + \frac{9}{7} = \frac{3}{7}
\][/tex]
Subtract [tex]\( \frac{9}{7} \)[/tex] from both sides of the equation to isolate the [tex]\( 3x \)[/tex] term:
[tex]\[
3x = \frac{3}{7} - \frac{9}{7}
\][/tex]
2. Simplify the right side:
[tex]\[
3x = \frac{3 - 9}{7}
\][/tex]
[tex]\[
3x = \frac{-6}{7}
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-6}{7} \div 3
\][/tex]
Dividing by 3 is the same as multiplying by its reciprocal, [tex]\( \frac{1}{3} \)[/tex]:
[tex]\[
x = \frac{-6}{7} \times \frac{1}{3}
\][/tex]
Multiply the numerators and the denominators:
[tex]\[
x = \frac{-6 \cdot 1}{7 \cdot 3}
\][/tex]
[tex]\[
x = \frac{-6}{21}
\][/tex]
4. Reduce the fraction:
The fraction [tex]\( \frac{-6}{21} \)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3:
[tex]\[
x = \frac{-6 \div 3}{21 \div 3}
\][/tex]
[tex]\[
x = \frac{-2}{7}
\][/tex]
So, the solution for the given equation is:
[tex]\[
x = -\frac{2}{7}
\][/tex]
