Question

Solving Equations Find all real solutions of the equation.

$\left|x-7\right|=4$

Short answer

The given equation has two real solutions$3$ and $11$.

Step-by-step solution

Step 1. Definition of equation and absolute equation.

Equation is a mathematical statement in which two expressions are equal to each other.

If an absolute equation is $\left|x\right|=a$, then $x=\pm a$.

Step 2. Given Information.

The given equation is:

$\left|x-7\right|=4$

Step 3. Solve the given equation.

The given equation can be written as:

$x-7=\pm 4$

Add$7$ on both sides.

$\begin{array}{c}x-7+7=\pm 4+7\\ x=7\pm 4\end{array}$

Now,

$\begin{array}{c}x=7-4\\ =3\end{array}$

And,

$\begin{array}{c}x=7+4\\ =11\end{array}$

Thus, the given equation has two real solutions$3$ and $11$.