We have the following inequality:
[tex]4(x+3)\leq44[/tex]And we have to solve it for x.
To solve the inequality, we can proceed as follows:
1. Apply the distributive property at the left side of the inequality:
[tex]\begin{gathered} 4(x)+4(3)\leq44 \\ \\ 4x+12\leq44 \end{gathered}[/tex]2. Subtract 12 from both sides of the inequality:
[tex]\begin{gathered} 4x+12-12\leq44-12 \\ \\ 4x\leq32 \end{gathered}[/tex]3. Divide both sides of the inequality by 4 as follows:
[tex]\begin{gathered} \frac{4x}{4}\leq\frac{32}{4} \\ \\ x\leq8 \end{gathered}[/tex]Therefore, in summary, the solution for the inequality is:
[tex]x\leq8[/tex][First option]