How do you solve #3|x+11|=24#?

Question

Genesis Allen · Accepted Answer

See a solution process below:

First, divide each side of the equation by #color(red)(3)# to isolate the absolute value function while keeping the equation balanced: #(3abs(x + 11))/color(red)(3) = 24/color(red)(3)# #(color(red)(cancel(color(black)(3)))abs(x + 11))/cancel(color(red)(3)) = 8# #abs(x + 11) = 8# Since the absolute value function takes any term and converts it to a non-negative form, we have to solve the term for both its positive and negative equivalent within the absolute value function. First Solution: #x + 11 = -8# #x + 11 - color(red)(11) = -8 - color(red)(11)# #x + 0 = -19# #x = -19# Option 2: #x + 11 = 8# #x + 11 - color(red)(11) = 8 - color(red)(11)# #x + 0 = -3# #x = -3# The Solutions Are: #x = -19# and #x = -3#

Eva Abramson · Answer

undefined To solve the equation $3\lvert x + 11 \rvert = 24$, you first isolate the absolute value expression by dividing both sides by 3, which gives you $\lvert x + 11 \rvert = 8$. Then, you split the equation into two cases: $x + 11 = 8$ and $x + 11 = -8$. Solve each case separately to find the solutions.

Case 1: $x + 11 = 8$
Subtract 11 from both sides: $x = 8 - 11 = -3$.

Case 2: $x + 11 = -8$
Subtract 11 from both sides: $x = -8 - 11 = -19$.

So, the solutions to the equation are $x = -3$ and $x = -19$.