vestirme4

2020-11-08

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

Nola Robson

Step 1
The absolute value equation has solution of -3 is,
$|x+3|=0$
Now the solution is.
$|x+3|=0$

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.
$|x-11|=0$

In both case the solution is 11.

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

Don Sumner

The absolute value equation with solutions -3 and 11 can be written as follows:
$|x-\frac{-3+11}{2}|=\frac{11-\left(-3\right)}{2}$
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, $\frac{11-\left(-3\right)}{2}$, 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

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:
$|x-\left(-3\right)|=0$ and $|x-11|=0$
In the first equation, the expression inside the absolute value brackets is $\left(x-\left(-3\right)\right)$, which represents the distance between $x$ and $-3$. Similarly, in the second equation, the expression inside the absolute value brackets is $\left(x-11\right)$, 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.

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