Question

what value or values of x satisfy 2|x + 5.3| = 4.2?
○ x can only equal - 3.2.
○ x can only equal 7.4.
○ x can equal - 3.2 or - 7.4.
○ x can equal - 3.2 or 7.4.

Explanation:

Step1: Isolate the absolute - value expression

Divide both sides of the equation $2|x + 5.3|=4.2$ by 2. We get $|x + 5.3|=\frac{4.2}{2}=2.1$.

Step2: Consider two cases

Case 1: $x+5.3 = 2.1$. Solve for $x$ by subtracting 5.3 from both sides. So $x=2.1−5.3=-3.2$.
Case 2: $x + 5.3=-2.1$. Solve for $x$ by subtracting 5.3 from both sides. So $x=-2.1−5.3=-7.4$.

Answer:

$x$ can equal - 3.2 or - 7.4.