Question

0,9/|2x + 0,7| =3/5​

Answer 1

Решение в приложении

Answer 2

To solve the equation $0.9 / |2x + 0.7| = 3/5$, you can follow these steps:

1. Start by isolating the absolute value expression on one side of the equation. To do this, you can multiply both sides by $|2x + 0.7|$ to get rid of the fraction on the left side:

   $0.9 = \frac{3}{5} \cdot |2x + 0.7|$

2. Now, you can get rid of the fraction on the right side by multiplying both sides by $5$:

   $5 \cdot 0.9 = 3 \cdot |2x + 0.7|$

   Simplify the left side:

   $4.5 = 3 \cdot |2x + 0.7|$

3. Divide both sides by $3$:

   $\frac{4.5}{3} = |2x + 0.7|$

   Simplify the left side:

   $1.5 = |2x + 0.7|$

4. Now, we need to consider two cases for the absolute value:

   Case 1: $2x + 0.7$ is positive or zero:

   If $2x + 0.7$ is positive or zero, then $|2x + 0.7|$ is equal to $2x + 0.7$. In this case, we have:

   $1.5 = 2x + 0.7$

   Subtract $0.7$ from both sides:

   $1.5 - 0.7 = 2x$

   $0.8 = 2x$

   Divide by $2$:

   $x = 0.4$

   So, one solution is $x = 0.4$ when $2x + 0.7$ is positive or zero.

   Case 2: $2x + 0.7$ is negative:

   If $2x + 0.7$ is negative, then $|2x + 0.7|$ is equal to $-(2x + 0.7)$. In this case, we have:

   $1.5 = -(2x + 0.7)$

   To isolate $-2x - 0.7$, subtract $1.5$ from both sides:

   $-2x - 0.7 = 1.5$

   Add $0.7$ to both sides:

   $-2x = 2.2$

   Divide by $-2$:

   $x = -1.1$

   So, the other solution is $x = -1.1$ when $2x + 0.7$ is negative.

Therefore, the solutions to the equation $0.9 / |2x + 0.7| = 3/5$ are $x = 0.4$ and $x = -1.1$.