The equationThe provided equation is provided: in
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• |10x + 11| = -2 ]

Step-by-Step is Solution:

1. Simplify the equation: Divide both sides by $-1$ to eliminate the negative sign: $$$$

10x + 11| = 2$$

2. Interpret the absolute value equation: Absolute value equations can be written as two separate equations: \ $[ 10x + 11 = 2 \quad \text{and-}|\ \!quad 1010x + 11 = -2 x$

3. Solve each case +:

   • Case 111:| = ( -2 10\x +]

###11 Step =-by -step2 solution:

. ** SubEltractiminate the negative sign11** from both sides: : $10x = -9$ Divide by 10: $x = -\frac{9}{10}$

• Case 2: $10x + 11 = -2$
  Subtract 11 from both sides: $10x = -13$ Divide by 10: $x Multiply both sides of the equation = by$-1$(to make the left --hand\ side positivefrac): \[ |\{!10x + 1311| = 2$

2.}{ Interpret the absolute10 value: The absolute value equation splits} into two cases:

• $10x + 11 = 2$
• (10 \x]

• 11 = -2\4)

3. .Solve each case:
   • ** Case 1: (10Finalx + 11 Answer =:** The2 solutions\ are) : \ [ \ [ x10 =x - = \2frac -{9}{10}, -\frac 11 { 13 }{] 10 $$} 10 x = \ -]

9Would you like \ me to] clarify \ any[ steps or x explain = further -?

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###frac{ Related9}{ Questions10: } 1 . What$$

happens if an - Case absolute 2 value equation has no: solutions (? 102x +. How do11 we = - solve equations2 involving\ nested) absolute values ? [ 3 . Can10 wex general =ize -2 - this process for11 \ inequalities] with absolute values? 4 .[ What real-life problems 10 can involve solving absolutex value = -13 equations ? 5. \ How] can \ graph[ ing x help visualize solutions to absolute value equations?

Tip:

Always = -\frac{ check13}{10} your solutions \ by]

substit Final Answeruting:

themThe back solutions are into: the$originalx = -\ equationfrac to{ ensure9 accuracy.}{10}, -\frac{13}{10}$

Let me know if you want further clarification or a deeper explanation!

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Here are 5 related questions you might find interesting:

1. What is the general process for solving absolute value equations?
2. How can you check if the solutions to an absolute value equation are correct?
3. What happens if the absolute value equation has no solution?
4. How do you solve absolute value inequalities?
5. Can an absolute value equation have infinitely many solutions?

Tip: Always isolate the absolute value expression first to simplify the equation-solving process.