Question

5. Решите уравнение: 7|x|+5|x|-3=2|x|+21пожалуйста помогите, соч!!​

Answer 1

Ответ:

7|х|+5|х|-2|х|=21+3

10|х|=24

|х|=2,4

{2,4; - 2,4}

Answer 2

Solving the Equation 7|x| + 5|x| - 3 = 2|x| + 21

To solve the equation 7|x| + 5|x| - 3 = 2|x| + 21, we can start by isolating the absolute value term on one side of the equation and then solving for the absolute value expression.

Step 1: Isolating the Absolute Value Term

First, let's combine like terms on both sides of the equation to simplify it:

7|x| + 5|x| - 3 = 2|x| + 21

This simplifies to:

12|x| - 3 = 2|x| + 21

Now, let's isolate the absolute value term by moving the constant term to the other side of the equation:

12|x| - 2|x| = 21 + 3

This simplifies to:

10|x| = 24

Step 2: Solving for the Absolute Value Expression

Now, we can solve for the absolute value expression by considering both the positive and negative cases.

For the positive case:

10x = 24 x = 24/10 x = 2.4

For the negative case:

10(-x) = 24 -10x = 24 x = -24/10 x = -2.4

So, the solutions for the equation 7|x| + 5|x| - 3 = 2|x| + 21 are x = 2.4 and x = -2.4.

Note: When solving absolute value equations, it's important to consider both the positive and negative cases for the absolute value expression.

I hope this helps! Let me know if you have further questions or need additional assistance.