Question

1)7/38-3x=2/9 2)1/3x-2/6=5/12

Answer 1

1/3х-2/6=5/12

1/3х=5/12+2/6

1/3х=5/12+4/12

1/3х=9/12

х=9/12/(1/3)

х=1/4

Answer 2

Let's solve these equations step by step:

1. $\frac{7}{38} - 3x = \frac{2}{9}$

First, we'll isolate $x$. Start by subtracting $\frac{7}{38}$ from both sides of the equation:

$-3x = \frac{2}{9} - \frac{7}{38}$

Now, find a common denominator for $\frac{2}{9}$ and $\frac{7}{38}$, which is 342. Rewrite both fractions with this denominator:

$-3x = \frac{76}{342} - \frac{63}{342}$

Now, subtract the fractions:

$-3x = \frac{76 - 63}{342}$

$-3x = \frac{13}{342}$

Now, divide both sides by -3 to solve for $x$:

$x = \frac{13}{342} \div (-3)$

$x = -\frac{13}{342} \div 3$

To simplify further, you can find the greatest common divisor (GCD) of 13 and 342, which is 1, and simplify the fraction:

$x = -\frac{13}{342} \div 3 \times \frac{1}{1} \div \frac{1}{1}$

$x = -\frac{13}{342} \times \frac{1}{3}$

$x = -\frac{13}{1026}$

2. $\frac{1}{3}x - \frac{2}{6} = \frac{5}{12}$

Start by simplifying the fractions:

$\frac{1}{3}x - \frac{1}{3} = \frac{5}{12}$

Now, add $\frac{1}{3}$ to both sides to isolate $x$:

$\frac{1}{3}x = \frac{5}{12} + \frac{1}{3}$

Find a common denominator for $\frac{5}{12}$ and $\frac{1}{3}$, which is 12, and rewrite both fractions:

$\frac{1}{3}x = \frac{5}{12} + \frac{4}{12}$

Now, add the fractions on the right side:

$\frac{1}{3}x = \frac{5 + 4}{12}$

$\frac{1}{3}x = \frac{9}{12}$

Now, simplify the fraction on the right side by finding the GCD of 9 and 12, which is 3:

$\frac{1}{3}x = \frac{9}{12} \div 3$

$\frac{1}{3}x = \frac{3}{4}$

Finally, multiply both sides by 3 to solve for $x$:

$x = \frac{3}{4} \times 3$