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sladkih [1.3K]
3 years ago
6

What value of x is in the solution set of 2x – 3 > 11 – 5x?

Mathematics
1 answer:
pochemuha3 years ago
4 0

Given:

2x -3 > 11 -5x

Simplify both sides:

2x - 3 > -5x + 11

Add 5x to both sides:

2x - 3 +5x > -5x + 11 +5

7x - 3 > 11

Add 3 to both sides:

7x - 3 +3 > 11 + 3

7x > 14

Divided 7 to both sides:

\frac{7x}{7} > \frac{14}{7}

x > 2

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Answer:

4.  Horizontal shrink by a factor of ¹/₅

5.  Left 5, Up 5

6.  Right 5, Down 5

Step-by-step explanation:

Transformations of Graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.

<u>Transformations</u>

For a > 0

f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}

f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}

f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}

f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}

y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a

y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}

y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}

y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}

Identify the transformations that take the parent function to the given function.

<u>Question 4</u>

\textsf{Parent function}: \quad f(x)=x^3

\textsf{Given function}: \quad f(x)=(5x)^3

Comparing the parent function with the given function, we can see that the <u>x-value of the parent function</u> has been <u>multiplied</u> by 5.

Therefore, the transformation is:

y=f(5x) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{5}

As a > 1, the transformation visually is a compression in the x-direction, so we can also say:  Horizontal shrink by a factor of ¹/₅

<u>Question 5</u>

\textsf{Parent function}: \quad f(x)=x^3

\textsf{Given function}: \quad f(x)=(x+5)^3+5

Comparing the parent function with the given function, we can see that there are a series of transformations:

<u>Step 1</u>

5 has been <u>added to the x-value</u> of the parent function.

f(x+5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units left}

<u>Step 2</u>

5 has then been <u>added to function</u>.

f(x+5)+5 \implies f(x+5) \: \textsf{translated}\:5\:\textsf{units up}

<u>Transformation</u>:  Left 5, Up 5

<u>Question 6</u>

\textsf{Parent function}: \quad f(x)=x^3

\textsf{Given function}: \quad f(x)=(x-5)^3-5

Comparing the parent function with the given function, we can see that there are a series of transformations:

<u>Step 1</u>

5 has been <u>subtracted from the x-value</u> of the parent function.

f(x-5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units right}

<u>Step 2</u>

5 has then been <u>subtracted from function</u>.

f(x-5)-5 \implies f(x-5) \: \textsf{translated}\:5\:\textsf{units down}

<u>Transformation</u>:  Right 5, Down 5

Learn more about graph transformations here:

brainly.com/question/27845947

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