Question

solve the equations.
(a) $|x + 1| = 4$
(b) $|x + 1| = 0$
(c) $|x + 1| = -6$
part 1 of 3
(a) the solution set of $|x + 1| = 4$ is .
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ℝ

Explanation:

Step1: Apply absolute value rule

For $|A|=B$ ($B>0$), $A=B$ or $A=-B$. So $x+1=4$ or $x+1=-4$.

Step2: Solve first equation

$x+1=4$
$x=4-1=3$

Step3: Solve second equation

$x+1=-4$
$x=-4-1=-5$

Step4: Solve equation (b)

For $|x+1|=0$, $x+1=0$, so $x=-1$.

Step5: Solve equation (c)

Absolute value can't be negative, so no solution.

Answer:

(a) The solution set of $|x+1|=4$ is $\{3, -5\}$
(b) The solution set of $|x+1|=0$ is $\{-1\}$
(c) The solution set of $|x+1|=-6$ is $\{\}$