Mathematics, 11.07.2019 16:40 shookie1993

Which number line represents the solutions to |x + 4| = 2?

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Answer from: lowrain

The number line for $\fbox{\begin\\\ \bf \text{option 1}\\\end{minispace}}$ represents the solution for the equation |x+4|=2 .

Further explanation:

The equation is given as follows:

|x+4|=2

In the above equation represents the modulus function.

Modulus function is defined as a function which gives positive value of the function for any real value of .

For example: The function y=|x| is a modulus function in which and or .

In the given equation |x+4| is a modulus expression.

There are two cases formed for |x+4| .

First case: x-4

If x-4 then $|x+4|\rightarrow (x+4)$ .

Substitute |x+4|=(x+4) in |x+4|=2 .

$\begin{aligned}x+4&=2\\x&=2-4\\&=-2\end{aligned}$

Therefore, for x-4 the value of which satisfies the equation |x+4|=2 is x=-2 .

Second case:

If then $|x+4|\rightarrow -(x+4)$ .

Substitute |x+4|=-(x+4) in |x+4|=2 .

$\begin{aligned}-(x+4)&=2\\-x-4&=2\\-x&=2+4\\-x&=6\\x&=-6\end{aligned}$

Therefore, for the value of which satisfies the equation |x+4|=2 is x=-6 .

This implies that the solution for the equation |x+4|=2 or the value of which satisfies the given equation are $\fbox{\begin\\\ \math x=-2\ \text{and}\ x=-6\\\end{minispace}}$ .

Option 1:

The number line in option 1 shows that the solutions of the equation |x+4|=2 are x=-2 and x=-6 .

As per our calculation made above the solutions for the equation |x+4|=2 are x=-2 and x=-6 .

This implies that option 1 is correct.

Option 2:

The number line in option 2 shows that the solutions of the equation |x+4|=2 are x=2 and x=4 .

As per our calculation made above the solutions for the equation |x+4|=2 are x=-2 and x=-6 .

This implies that option 2 is incorrect.

Option 3:

The number line in option 3 shows that the solutions of the equation |x+4|=2 are x=2 and x=6 .

As per our calculation made above the solutions for the equation |x+4|=2 are x=-2 and x=-6 .

This implies that option 3 is incorrect.

Option 4:

The number line in option 4 shows that the solutions of the equation |x+4|=2 are x=-2 and x=-4 .

As per our calculation made above the solutions for the equation |x+4|=2 are x=-2 and x=-6 .

This implies that option 4 is incorrect.

Therefore, the number line for $\fbox{\begin\\\ \bf \text{option 1}\\\end{minispace}}$ represents the solution for the equation |x+4|=2 .

Learn more:

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2.A problem to find radius and center of circle link

3.A problem to determine intercepts of a line link

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Functions

Keywords: Functions, modulus, modulus function, number line, real line, |x+4|=2, equation, root, zeroes, solutions, absolute function, x=-6 and x=-2.

Answer from: Quest

The answer to your question is 1/9

Answer from: Quest

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743

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