Solve the inequality for v: 16 > -13 + v. Simplify your answer as much as possible.
Understand the Problem
The question asks us to solve the inequality 16 > -13 + v for the variable 'v'. This involves isolating 'v' on one side of the inequality to find the range of values that 'v' can take.
Answer
$v < 29$
Answer for screen readers
$v < 29$
Steps to Solve
- Isolate $v$ by adding 13 to both sides of the inequality
To isolate $v$, we need to eliminate the -13 term from the right side of the inequality. We can do this by adding 13 to both sides: $16 + 13 > -13 + v + 13$
- Simplify both sides
Now, simplify both sides of the inequality: $29 > v$
So the solution to the inequality is $29 > v$, which can also be written as $v < 29$.
$v < 29$
More Information
The solution $v < 29$ means that any value of $v$ that is less than 29 will satisfy the original inequality. For example, if $v = 0$, then $16 > -13 + 0$ which simplifies to $16 > -13$, which is true.
Tips
A common mistake is forgetting to add 13 to both sides of the inequality, or only adding it to one side. Another common mistake is to switch the direction of the inequality sign when it's not necessary. The direction of the inequality sign only needs to be flipped if you multiply or divide both sides by a negative number, which we did not need to do in this case.
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