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denis23 [38]
2 years ago
13

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

Mathematics
2 answers:
horrorfan [7]2 years ago
3 0

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

nasty-shy [4]2 years ago
3 0

\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:)}

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