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notsponge [240]
3 years ago
9

Solve the equation. Check for extraneous solutions. Type your answers in the blanks. Show your work. |4x+3| = 9+2x

Mathematics
1 answer:
GaryK [48]3 years ago
3 0

Answer:

Step-by-step explanation:

|4x + 3| = 9 + 2x

We see the absolute value so we have to consider 2 cases:

(1)

4x + 3 = -9 - 2x

6x = -12

x = -2

(2)

4x + 3 = 9 + 2x

2x = 6

x = 3

Let's plug in both results.

|4(-2) + 3| = 9 + 2(-2)

|-5| = 9 - 4

5 = 5

Therefore x = -2 is a solution

|4(3) + 3| = 9 + 2(3)

|15| = 9 + 6

15 = 15

Therefore x = 3 is also a solution.

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Considering the definition of the absolute value function, the expression is written as -7m + 56.

<h3>What is the definition of the absolute value function?</h3>

The absolute value function is defined as follows:

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That is, where the expression is negative, it is multiplied by -1, while where it is not negative the expression is kept.

In this problem, the expression is:

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7(0) - 56 = -56.

The expression is negative, hence the signal is changed, that is:

|7m - 56| = -(7m - 56) = -7m + 56.

More can be learned about the absolute value function at brainly.com/question/24734454

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Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

f(x) = 5x + 7

g(x) = 3x - 1

<u>Step 2: Find</u>

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