Given: An absolute inequality
[tex]\lvert{2x+3}\rvert=15[/tex]
Required: To solve the given absolute inequality.
Explanation: The absolute rule states
[tex]\begin{gathered} If\text{ }\lvert{x}\rvert=a,\text{ }a>0\text{ ,then} \\ x=a\text{ or }x=-a \end{gathered}[/tex]
Hence for the given problem, we have
[tex]2x+3=15\text{ or }2x+3=-15[/tex]
Solving these two equations
[tex]\begin{gathered} 2x=12\text{ or }2x=-18 \\ \end{gathered}[/tex]
Which gives the value of x as
[tex]x=6\text{ or }x=-9[/tex]
Hence the equation given can have two solutions.
Final Answer: The given equation can have two solutions as x=6 or x=-9.
