Question

How do you solve \[3q+11+8q>99\]?

Answer 1

Hint: In this problem, we have to solve the given inequality and find the value of q. We should know that, to solve this type of problems, we can just simplify as we do in an equation. In an equation it exactly gives a value, but in an inequality it doesn’t give an exact value. We can first subtract -11 on both sides, add the terms with q and simply the remaining steps to get the value of q.

Complete step by step answer:
We know that the given inequality to be simplified is,
 \[3q+11+8q>99\]
Now we can subtract the number -11 on both the left-hand side and right-hand side of the given inequality, we get
\[\begin{align}
  & \Rightarrow 3q+11+8q-11>99-11 \\
 & \Rightarrow 3q+8q>88 \\
\end{align}\]
Now we can add the terms with q in the left-hand side of the above inequality, we get
\[\Rightarrow 11q>88\]
We can now divide by the number 11 on both the left-hand side and right-hand side of the given inequality, we get
\[\Rightarrow \dfrac{11q}{11}>\dfrac{88}{11}\]
We can now cancel the similar terms in the above inequality, we get
\[\Rightarrow q>8\]
Therefore, on solving the given inequality \[3q+11+8q>99\], the value is \[q>8\].

Note:
Students make mistakes while simplifying an inequality. We should know that, to solve this type of problems we should know to differentiate between an inequality and an equation and know how to solve a problem in an equality. Students make mistakes in writing the correct symbol, which should be concentrated.