Question

What is the answer for this equation |v + 4| ≤ 10

Answer 1

Step 1. The expression that we have is:

`|v+4|\leq10`

And we need to solve for v.

Step 2. To solve this problem we use the following rule for absolute value expressions:

`\begin{gathered} |x|\leq b \\ \downarrow \\ -b\leq x\leq b \end{gathered}`

In our case:

`\begin{gathered} \lvert v+4\rvert\leqslant10 \\ \downarrow \\ -10\leq v+4\leqslant10 \end{gathered}`

Step 3. The final step to solve is to subtract 4 to all parts of the expression:

`\begin{gathered} -10\leqslant v+4\leqslant10 \\ \downarrow \\ -10-4\leqslant v+4-4\leqslant10-4 \\ \downarrow \\ \boxed{-14\leqslant v\leqslant6} \end{gathered}`

Answer:

`\boxed{-14\leqslant v\leqslant6}`