Question

2) 5|x] – 3|x| = 33;4)42-63|х|=65|х|​

Answer 1

Ответ:

2) 2|x|=33,  |x|=16,5,  x=16,5  или  x=-16,5

4) 42=63|x|+65|x|,  42=128|x|,  |x|=42/128,   |x|=21/64,  x=21/64  или  x= -21/64

Пошаговое объяснение:

Answer 2

Let's solve these two absolute value equations:

1. $5|x| - 3|x| = 33$

To solve this equation, combine like terms:

$2|x| = 33$

Now, divide both sides by 2 to isolate $|x|$:

$|x| = \frac{33}{2}$

Now, we have two cases to consider, one for $x$ being positive and one for $x$ being negative:

Case 1: $x$ is positive: $x = \frac{33}{2}$

Case 2: $x$ is negative: $-x = \frac{33}{2}$

Now, multiply both sides of the equation by -1 to isolate $x$:

$x = -\frac{33}{2}$

So, there are two solutions to the equation: $x = \frac{33}{2}$ and $x = -\frac{33}{2}$.

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2. $42 - 63|x| = 65|x|$

To solve this equation, first isolate the absolute value term on one side:

$42 = (65 + 63)|x|$

Combine the numbers on the right side:

$42 = 128|x|$

Now, divide both sides by 128 to isolate $|x|$:

$|x| = \frac{42}{128}$

Simplify the fraction:

$|x| = \frac{21}{64}$

Again, we have two cases to consider:

Case 1: $x$ is positive: $x = \frac{21}{64}$

Case 2: $x$ is negative: $-x = \frac{21}{64}$

Multiply both sides of the equation by -1 to isolate $x$:

$x = -\frac{21}{64}$

So, there are two solutions to the equation: $x = \frac{21}{64}$ and $x = -\frac{21}{64}$.