Step 1. The expression that we have is:
[tex]|v+4|\leq10[/tex]
And we need to solve for v.
Step 2. To solve this problem we use the following rule for absolute value expressions:
[tex]\begin{gathered} |x|\leq b \\ \downarrow \\ -b\leq x\leq b \end{gathered}[/tex]
In our case:
[tex]\begin{gathered} \lvert v+4\rvert\leqslant10 \\ \downarrow \\ -10\leq v+4\leqslant10 \end{gathered}[/tex]
Step 3. The final step to solve is to subtract 4 to all parts of the expression:
[tex]\begin{gathered} -10\leqslant v+4\leqslant10 \\ \downarrow \\ -10-4\leqslant v+4-4\leqslant10-4 \\ \downarrow \\ \boxed{-14\leqslant v\leqslant6} \end{gathered}[/tex]
Answer:
[tex]\boxed{-14\leqslant v\leqslant6}[/tex]
