161k views
5 votes
What is the solution of 2|2x-1|-8=18?

User Georgemp
by
8.1k points

2 Answers

3 votes

➣ Assignment:
\bold2x-1\right

↔↔↔↔↔↔↔↔

➣ Answer:
\boxed{\bold{x=-6, \ x=7}}

↔↔↔↔↔↔↔↔

Explanation: ↓↓↓↓↓

↔↔↔↔↔↔↔↔

➤ [ Step One ] Add 8 To Both Sides


\bold2\left

➤ [ Step Two ] Simplify


\bold2\left

➤ [ Step Three ] Divide Both Sides By 2


\bold2x-1\right

➤ [ Step Four ] Simplify


\bold=13

➤ [ Step Five ] Apply Absolute Rule

Note:
\bold{Absolute \ Rule: \ \mathrm{If}\:|u|\:=\:a,\:a>0\:\mathrm{then}\:u\:=\:a\:\quad \mathrm{or}\quad \:u\:=\:-a}


\bold{2x-1=-13\quad \mathrm{or}\quad \:2x-1=13}

➤ [ Step Six ] Simplify Equations


\bold{2x-1=-13: \ x=-6}


\bold{2x-1=13: \ x \ = \ 7}

➤ [ Step Seven ] Combine Solutions


\bold{x=-6, \ x=7}

↔↔↔↔↔↔↔↔


\bold{\rightarrow Mordancy \leftarrow}

User Victorf
by
7.9k points
4 votes

Solve for
|2x-1|:


2|2x-1|-8=18\implies2|2x-1|=26\implies|2x-1|=13

Now if
2x-1\ge0, we have
|2x-1|=2x-1 and


2x-1=13\implies2x=14\implies x=7

On the other hand, if
2x-1<0, then
|2x-1|=-(2x-1)=1-2x and


1-2x=13\implies-2x=12\implies x=-6

User ITO Yosei
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories