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

Asked by maham237 @ 17/12/2020 in Mathematics viewed by 464 People

Answered by maham237 @ 17/12/2020

The given equation is,

|x + 4| = 2

To solve an absolute value equation , first step is to remove the absolute value sign.

An absolute vaue always give a positive result whether the expression inside the absolute sign is positive or negative.

Hence, to remove an absolute value we will take both positive an negative. Therefore,

x + 4 = 2 and x + 4 = - 2.

So, x = 2 -4 and -2 - 4.

x = -2 and -6.

So, first choice is correct.

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 $x$ .

For example: The function $y=|x|$ is a modulus function in which $y>0$ and $x$ or $x>0$ .

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 $x$ which satisfies the equation $|x+4|=2$ is $x=-2$ .

Second case: $x$

If $x$ 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 $x$ the value of $x$ 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 $x$ 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:

1. A problem on composite function brainly.com/question/2723982

2. A problem to find radius and center of circle brainly.com/question/9510228

3. A problem to determine intercepts of a line brainly.com/question/1332667

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.

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

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