Question

1/9(7х-3)-1/6(4х+3)=х-2

Answer 1

1/9(7х-3)-1/6(4х+3)=х-2

-5/6 + х/9 = х-2

(-8)х/9 = - 7/6

х = 21/16

Answer 2

To solve the given equation for the variable $x$, follow these steps:

Given equation: $\frac{1}{9}(7x-3) - \frac{1}{6}(4x+3) = x - 2$

Step 1: Distribute the fractions on both sides of the equation. $\frac{7x}{9} - \frac{3}{9} - \frac{4x}{6} - \frac{3}{6} = x - 2$

Step 2: Simplify the fractions. $\frac{7x - 3}{9} - \frac{2x + 3}{6} = x - 2$

Step 3: Get rid of the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators, which is 18 (the least common multiple of 9 and 6). $18 \cdot \left(\frac{7x - 3}{9}\right) - 18 \cdot \left(\frac{2x + 3}{6}\right) = 18 \cdot (x - 2)$

Simplify each term: $2(7x - 3) - 3(2x + 3) = 18x - 36$ $14x - 6 - 6x - 9 = 18x - 36$

Step 4: Combine like terms on both sides of the equation. $14x - 6x - 6 - 9 = 18x - 36$ $8x - 15 = 18x - 36$

Step 5: Move all the terms involving $x$ to one side of the equation by subtracting $8x$ and adding $36$ to both sides. $-15 + 36 = 18x - 8x$ $21 = 10x$

Step 6: Solve for $x$ by dividing both sides by $10$. $x = \frac{21}{10}$

So, the solution for the equation is $x = \frac{21}{10}$, which can be written as a mixed number $x = 2\frac{1}{10}$.