Question

4|x| +5 |x|-3=2|x|+11​

Answer 1

Ответ:

-2; 2

Пошаговое объяснение:

4|x|+ 5|x|-3= 2|x|+11

9|x|- 2|x|=11+3

7|x|=14

|x|= 14/7

|x|= 2

x1= 2                 x2= -2

Answer 2

To solve the equation $4|x| + 5|x| - 3 = 2|x| + 11$, you can start by simplifying it step by step.

First, combine like terms on both sides of the equation:

$4|x| + 5|x| - 3 = 2|x| + 11$

Combine the $|x|$ terms on each side:

$(4 + 5)|x| - 3 = (2)|x| + 11$

$9|x| - 3 = 2|x| + 11$

Next, move the $2|x|$ term to the left side by subtracting it from both sides of the equation:

$9|x| - 2|x| - 3 = 11$

Now, combine the $|x|$ terms on the left side:

$(9 - 2)|x| - 3 = 11$

$7|x| - 3 = 11$

Now, add 3 to both sides to isolate the $7|x|$ term:

$7|x| = 14$

Finally, divide both sides by 7 to solve for $|x|$:

$\frac{7|x|}{7} = \frac{14}{7}$

$|x| = 2$

Now that you've found $|x| = 2$, you need to consider both positive and negative values for $x$ because absolute value can be positive or negative. So, you have two possible solutions:

1. $x = 2$ (when $|x| = 2$)
2. $x = -2$ (when $|x| = 2$)

So, the equation has two solutions: $x = 2$ and $x = -2$.