Question

5|x +9| < 10 x< ? x> ?

Answer 1

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

Answer 2

$\huge\textsf{Hey there!}$

$\huge\textbf{Equation:}$

$\mathbf{5|x + 9| < 10}$

$\huge\textbf{Solving:}$

$\mathbf{5|x + 9| < 10}$

$\huge\textbf{DIVIDE 5 to BOTH SIDES:}$

$\mathbf{\dfrac{5|x \ + \ 9|}{5} = \dfrac{10}{5}}$

$\huge\textbf{Simplify it!}$

$\mathbf{|x + 9| < 2}$

$\huge\textbf{Solve the absolute value:}$

$\mathbf{|x + 9| < 2}$

$\huge\textbf{Possibly we know that:}$

$\mathbf{x + 9 < 2 \ and\ we\ know\ that \ x+9 > -2}$

$\huge\textbf{Solving for:}$

$\mathbf{x + 9 < 2}$

$\huge\textbf{SUBTRACT 9 to BOTH SIDES:}$

$\mathbf{x + 9 - 9 < 2 -9}$

$\huge\textbf{Simplify it!}$

$\mathbf{x < -7}$

$\huge\textbf{Solving for:}$

$\mathbf{x + 9 > -2}$

$\huge\textbf{SUBTRACT 9 to BOTH SIDES:}$

$\mathbf{x + 9 - 9 > -2 - 9}$

$\huge\textbf{Simplify it!}$

$\mathbf{x > -11}$

$\huge\textbf{Answer(s):}$

$\huge\boxed{\mathsf{x < -7\ or\ x > -11}}\huge\checkmark$

$\huge\text{Good luck on your assignment \& enjoy your day!}$

~$\frak{Amphitrite1040:)}$