Question

5|x-4|=135 решения пжжжжж

Answer 1

Разделим обе части на 5
$|x - 4| = 27$

x-4=27; x = 27 + 4; x = 31
или
x-4= -27; x = -27 + 4; x = -23

Answer 2

To find the solutions to the equation $5|x-4| = 135$, we need to isolate the absolute value term and solve for $x$. Remember that the absolute value of a number is always non-negative, so we'll have two cases to consider: one where $x-4$ is positive and one where $x-4$ is negative.

Case 1: $x-4$ is positive (i.e., $x-4 \geq 0$)

When $x-4$ is positive, the equation becomes:

$5(x-4) = 135$

Now, solve for $x$:

$5x - 20 = 135$

$5x = 135 + 20$

$5x = 155$

$x = \frac{155}{5}$

$x = 31$

So, for this case, $x = 31$ is a solution.

Case 2: $x-4$ is negative (i.e., $x-4 < 0$)

When $x-4$ is negative, the equation becomes:

$5(-(x-4)) = 135$

Now, solve for $x$:

$5(-x + 4) = 135$

$-5x + 20 = 135$

$-5x = 135 - 20$

$-5x = 115$

$x = \frac{115}{-5}$

$x = -23$

So, for this case, $x = -23$ is a solution.

Therefore, the solutions to the equation $5|x-4| = 135$ are $x = 31$ and $x = -23$.