Write an absolute value equation that has solutions of -3 and 11.

Question

Nola Robson · Accepted Answer

Step 1
The absolute value equation has solution of -3 is,

| x + 3 | = 0

Now the solution is.

| x + 3 | = 0

- (x + 3) = 0 and x + 3 = 0

- x - 3 = 0 and x = - 3

- x = 3 and x = - 3

x = - 3 and x = - 3

In both case the solution is -3
Step 2
The absolute value equation has solution of 11 is,

| x - 11 | = 0

Now the solution is.

| x - 11 | = 0

- (x - 11) = 0 and x - 11 = 0

- x + 11 = 0 and x = 11

- x = - 11 and x = 11

x = 11 and x = 11

In both case the solution is 11.

madeleinejames20 · Accepted Answer

Result:|x+3|=11Explanation:To write an absolute value equation that has solutions of -3 and 11, we can use the form:|x−a|=bwhere &#039;a&#039; represents the value that the expression inside the absolute value brackets should equal, and &#039;b&#039; represents the solutions of the equation. In this case, the given solutions are -3 and 11. Therefore, we have:|x−(−3)|=11Simplifying further:|x+3|=11Thus, the absolute value equation that has solutions of -3 and 11 is |x+3|=11.

Don Sumner · Accepted Answer

The absolute value equation with solutions -3 and 11 can be written as follows:

| x - \frac{- 3 + 11}{2} | = \frac{11 - (- 3)}{2}

In this equation, the expression

x - \frac{- 3 + 11}{2}

represents the distance between

x

and the midpoint of the solutions -3 and 11. The right side of the equation,

\frac{11 - (- 3)}{2}

, represents half the distance between the two solutions. By setting the absolute value of the left side equal to the right side, we ensure that

x

is at an equal distance from both -3 and 11.

Eliza Beth13 · Accepted Answer

To write the absolute value equation with solutions -3 and 11, we can use the definition of absolute value. The absolute value of a number is its distance from zero on the number line. So, an absolute value equation with solutions -3 and 11 can be written as:

| x - (- 3) | = 0

and

| x - 11 | = 0

In the first equation, the expression inside the absolute value brackets is

(x - (- 3))

, which represents the distance between

x

and

- 3

. Similarly, in the second equation, the expression inside the absolute value brackets is

(x - 11)

, representing the distance between

x

and

11

.
Since the absolute value of a number is always non-negative, the only way for the absolute value to be equal to zero is when the expression inside the brackets is equal to zero. Therefore, the solutions to these equations are

x = - 3

and

x = 11

, respectively.

Write an absolute value equation that has solutions of -3 and 11.

Answered question

Answer & Explanation

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