Question

-|7/8|x+|-7/3|x+5/3=-2/3​

Answer 1

Ответ: -16/75

Пошаговое объяснение:

-7x/8 + (-7/3x) + 5/3=-2/3

-16/24•24/75=-16/75

Answer 2

To solve the equation $\left| \frac{7}{8}x \right| + \left| -\frac{7}{3}x + \frac{5}{3} \right| = -\frac{2}{3}$, you can break it down into several cases based on the absolute value expressions.

Case 1: $\frac{7}{8}x$ and $-\frac{7}{3}x + \frac{5}{3}$ are both non-negative. In this case, you can rewrite the equation without absolute values:

$\frac{7}{8}x - \left(-\frac{7}{3}x + \frac{5}{3}\right) = -\frac{2}{3}$

Now, solve for $x$:

$\frac{7}{8}x + \frac{7}{3}x - \frac{5}{3} = -\frac{2}{3}$

Combine like terms:

$\frac{7}{8}x + \frac{7}{3}x = \frac{5}{3} - \frac{2}{3}$

$\frac{7}{8}x + \frac{7}{3}x = \frac{3}{3}$

$\frac{7}{8}x + \frac{7}{3}x = 1$

Now, find a common denominator:

$\frac{21}{24}x + \frac{56}{24}x = 1$

Combine the fractions:

$\frac{21x + 56x}{24} = 1$

$\frac{77x}{24} = 1$

Now, isolate $x$:

$77x = 24$

$x = \frac{24}{77}$

Case 2: $\frac{7}{8}x$ is non-negative, but $-\frac{7}{3}x + \frac{5}{3}$ is negative. In this case, rewrite the equation without absolute values:

$\frac{7}{8}x - \left(\frac{7}{3}x - \frac{5}{3}\right) = -\frac{2}{3}$

Solve for $x$:

$\frac{7}{8}x - \frac{7}{3}x + \frac{5}{3} = -\frac{2}{3}$

Combine like terms:

$\frac{7}{8}x - \frac{21}{24}x + \frac{5}{3} = -\frac{2}{3}$