27. solve: 2|x + 1|-3 = 7
27. solve: 2|x + 1|-3 = 7
Answer
Explanation:
Step1: Isolate the absolute - value term
Add 3 to both sides of the equation $2|x + 1|-3 = 7$. $2|x + 1|=7 + 3$ $2|x + 1|=10$ Then divide both sides by 2: $|x + 1| = 5$.
Step2: Solve for two cases
Case 1: When $x+1\geq0$ (i.e., $x\geq - 1$), the equation becomes $x + 1=5$. Subtract 1 from both sides: $x=5 - 1$, so $x = 4$. Case 2: When $x + 1<0$ (i.e., $x<-1$), the equation becomes $-(x + 1)=5$. Expand the left - hand side: $-x-1 = 5$. Add 1 to both sides: $-x=5 + 1$, so $-x=6$. Multiply both sides by - 1: $x=-6$.
Answer:
$x = 4$ or $x=-6$