Question

5|x +9| < 10



x< ?
x> ?

Answer 1

x<−7 and x>−11

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 < 10`

`\huge\textbf{Solving:}`

`\mathbf < 10`

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

`\mathbf(5`

`\huge\textbf{Simplify it!}`

`\mathbfx + 9`

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

`\mathbf`

`\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`

~
`\frak{Amphitrite1040:)}`