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3 years ago

Solve the absolute value equation (picture listed below)

Mathematics

1 answer:

STALIN [3.7K]3 years ago

3 0

Answer:

17) x = 0, -6

18) x = 2, -4

Step-by-step explanation:

Isolate the absolute value, then split into 2 equations and solve both

example: |x + 1| = 2

x + 1 = 2, x + 1 = -2

x = 1, -3

------------------------------------

17) |x + 3| - 1 = 2

isolate the absolute value:

|x + 3| = 3

x + 3 = 3, x + 3 = -3

x = 0, -6

-----------------------------------------

18) 3|x + 1| = 9

isolate absolute value:

|x + 1| = 3

x + 1 = 3, x + 1 = -3

x = 2, -4

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Illusion [34]

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$x=-2,0,3$

Step-by-step explanation:

We have been given a function $f(x)=15x^3-15x^2-90x$ . We are asked to find the zeros of our given function.

To find the zeros of our given function, we will equate our given function by 0 as shown below:

$15x^3-15x^2-90x=0$

Now, we will factor our equation. We can see that all terms of our equation a common factor that is $15x$ .

Upon factoring out $15x$ , we will get:

$15x(x^2-x-6)=0$

Now, we will split the middle term of our equation into parts, whose sum is $-1$ and whose product is $-6$ . We know such two numbers are $-3\text{ and }2$ .

$15x(x^2-3x+2x-6)=0$

$15x((x^2-3x)+(2x-6))=0$

$15x(x(x-3)+2(x-3))=0$

$15x(x-3)(x+2)=0$

Now, we will use zero product property to find the zeros of our given function.

$15x=0\text{ (or) }(x-3)=0\text{ (or) }(x+2)=0$

$15x=0\text{ (or) }x-3=0\text{ (or) }x+2=0$

$\frac{15x}{15}=\frac{0}{15}\text{ (or) }x-3=0\text{ (or) }x+2=0$

$x=0\text{ (or) }x=3\text{ (or) }x=-2$

Therefore, the zeros of our given function are $x=-2,0,3$ .

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