Question

(x+1):6+(2-x):8=1:4+(x-3):12

Answer 1

Умножим каждое слагаемое в уравнении на 24.
4(х+1)+3(2-х)=6+2(х-3);
4х+4+6-3х=6+2х-6;
х+10=2х;
х=10.

ответ:10.

Answer 2

To solve the equation $\frac{x+1}{6} + \frac{2-x}{8} = \frac{1}{4} + \frac{x-3}{12}$, you can follow these steps:

Step 1: Find a common denominator for all fractions in the equation. In this case, the common denominator is 24 because it's the least common multiple of 6, 8, and 12.

Step 2: Rewrite each fraction with the common denominator of 24:

$\frac{(x+1) \cdot 4}{6 \cdot 4} + \frac{(2-x) \cdot 3}{8 \cdot 3} = \frac{1 \cdot 6}{4 \cdot 6} + \frac{(x-3) \cdot 2}{12 \cdot 2}$

Step 3: Simplify the fractions:

$\frac{4(x+1)}{24} + \frac{3(2-x)}{24} = \frac{6}{24} + \frac{2(x-3)}{24}$

Step 4: Now, the equation becomes:

$\frac{4(x+1)}{24} + \frac{3(2-x)}{24} = \frac{6}{24} + \frac{2(x-3)}{24}$

Step 5: Combine the fractions on both sides of the equation:

$\frac{4(x+1) + 3(2-x)}{24} = \frac{6 + 2(x-3)}{24}$

Step 6: Distribute and simplify the expressions in the numerators:

$\frac{4x + 4 + 6 - 3x}{24} = \frac{6 + 2x - 6}{24}$

Step 7: Combine like terms:

\frac(x + 10 - 3x}{24} = \frac(2x}{24}

Step 8: Further simplify:

$\frac{-2x + 10}{24} = \frac{2x}{24}$

Step 9: To eliminate the fractions, multiply both sides of the equation by 24:

$-2x + 10 = 2x$

Step 10: Move the $2x$ term to the left side of the equation by adding $2x$ to both sides:

$-2x + 10 + 2x = 2x + 2x$

Step 11: Simplify:

$10 = 4x$

Step 12: Divide by 4 to isolate $x$:

$x = \frac{10}{4}$

Step 13: Simplify the right side:

$x = \frac{5}{2}$

So, the solution to the equation is $x = \frac{5}{2}$.