Answer:
x<−7 and x>−11
Step-by-step explanation:
Let's solve your inequality step-by-step.
5(|x+9|)<10
Step 1: Divide both sides by 5.
5(|x+9|)/5 < 10/5
|x+9|<2
Step 2: Solve Absolute Value.
|x+9|<2
We know x+9<2 and x+9>−2
x+9<2(Condition 1)
x+9−9<2−9(Subtract 9 from both sides)
x<−7
x+9>−2(Condition 2)
x+9−9>−2−9(Subtract 9 from both sides)
x>−11
Answer:
x<−7 and x>−11
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathbf{5|x + 9| < 10}[/tex]
[tex]\huge\textbf{Solving:}[/tex]
[tex]\mathbf{5|x + 9| < 10}[/tex]
[tex]\huge\textbf{DIVIDE 5 to BOTH SIDES:}[/tex]
[tex]\mathbf{\dfrac{5|x \ + \ 9|}{5} = \dfrac{10}{5}}[/tex]
[tex]\huge\textbf{Simplify it!}[/tex]
[tex]\mathbf{|x + 9| < 2}[/tex]
[tex]\huge\textbf{Solve the absolute value:}[/tex]
[tex]\mathbf{|x + 9| < 2}[/tex]
[tex]\huge\textbf{Possibly we know that:}[/tex]
[tex]\mathbf{x + 9 < 2 \ and\ we\ know\ that \ x+9 > -2}[/tex]
[tex]\huge\textbf{Solving for:}[/tex]
[tex]\mathbf{x + 9 < 2}[/tex]
[tex]\huge\textbf{SUBTRACT 9 to BOTH SIDES:}[/tex]
[tex]\mathbf{x + 9 - 9 < 2 -9}[/tex]
[tex]\huge\textbf{Simplify it!}[/tex]
[tex]\mathbf{x < -7}[/tex]
[tex]\huge\textbf{Solving for:}[/tex]
[tex]\mathbf{x + 9 > -2}[/tex]
[tex]\huge\textbf{SUBTRACT 9 to BOTH SIDES:}[/tex]
[tex]\mathbf{x + 9 - 9 > -2 - 9}[/tex]
[tex]\huge\textbf{Simplify it!}[/tex]
[tex]\mathbf{x > -11}[/tex]
[tex]\huge\textbf{Answer(s):}[/tex]
[tex]\huge\boxed{\mathsf{x < -7\ or\ x > -11}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
