Question

1) 5|х|-4=|х| 2) |х|-5=3|х|

Answer 1

Пошаговое объяснение:

$|x| - 5 = 3 |x| \\ |x| - 3 |x| = 5 \\ - 2 |x| = 5$

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$5 |x| - 4 = |x| \\ 5 |x| - |x| = 4 \\ 4 |x| = 4 \\ |x| = 1 \\ x1 = 1 \\ x2 = - 1$

Answer 2

Let's solve each equation step by step:

1. $5|x| - 4 = |x|$

First, isolate the absolute value term:

$5|x| - |x| = 4$

Combine like terms:

$4|x| = 4$

Divide both sides by 4:

$|x| = 1$

Now, consider both the positive and negative solutions for $x$:

$x = 1 \text{ or } x = -1$

So, the solution set for the first equation is $x = 1$ or $x = -1$.

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2. $|x| - 5 = 3|x|$

Again, isolate the absolute value term:

$-2|x| = 5$

Divide both sides by -2:

$|x| = -\frac{5}{2}$

The absolute value of a number cannot be negative, so there are no real solutions for this equation. The solution set is empty or, in other words, there are no values of $x$ that satisfy the second equation.