How many cases do you have after you remove the absolute value?
Solutions: d=- 5 and d=5 Number Line:
Practice makes perfect
An absolute value measures an expression's distance from a midpoint on a number line.
|- 3d|= 15
This equation means that the distance is 15, either in the positive direction or the negative direction.
\begin{gathered}
|\text{-} 3d|={\color{#0000FF}{15}}\quad\Rightarrow\quadl- 3d= 15 - 3d= - 15
\end{gathered}
To find the solutions to the absolute value equation, we need to solve both of these cases for d.
|- 3d|=15
lc - 3d ≥ 0:- 3d = 15 & (I) - 3d < 0:- 3d = - 15 & (II)
lc- 3d=15 & (I) - 3d=- 15 & (II)
(I), (II): .LHS /(- 3).=.RHS /(- 3).
ld_1=- 5 d_2=5
Both - 5 and 5 are solutions to the absolute value equation. Let's graph these solutions on a number line.
<jsxgpre id="Solution17101" static=1>
var b=mlg.board([-5.7,1.5,5.7,-1.5],{"desktopSize":"medium", "style":"usa"});
b.po
int(-5,0);
b.point(5,0);
var numline1 = b.numline(1,0);
</jsxgpre>
