Question

How do you solve \[9h + 2 < - 79?\] .

Answer 1

Hint: In this question we solve single linear inequalities and follow pretty much the same process for solving linear equations. We will simplify both sides, get all the terms with the variable on one side and the numbers on the other side, and then multiply or divide both sides by the coefficient of the variable to get the solution.

Complete step-by-step solution:
It is given \[9h + 2 < - 79\]
To find the inequality of $ h $ from the given linear inequality:
First, we rearrange the equation by subtracting what is to the right of the great than sign from both sides of the inequality and we get
 $ \Rightarrow 9h + 2 - \left( { - 79} \right) < 0 $
Next, we adding the numbers in left hand side (LHS) and we get
 $ \Rightarrow 9h + 81 < 0 $
Then, we pulling out like factors in the above equation and we get
 $ \Rightarrow 9\left( {h + 9} \right) < 0 $
Now, we divide both sides by 9 and we get
 \[ \Rightarrow \dfrac{9}{9}\left( {h + 9} \right) < \dfrac{0}{9}\]
Next, we cancel the number 9 on the left hand side (LHS).
Here, $ \dfrac{0}{9} = 0 $ . And we get
 \[ \Rightarrow \left( {h + 9} \right) < 0\]
Now, we subtract 9 from both sides in the above equation and we get the final answer:
  $ \Rightarrow h + 9 - 9 < 0 - 9 $
Then, we eliminate 9 in the above equation:
On rewriting we get
 $ \Rightarrow h < - 9 $

Finally, the result can be shown in inequality form:
 $ \Rightarrow h < - 9 $ is the solution.
The interval notation is $ h \in \left( { - \infty , - 9} \right) $

Note: We have to mind that, a linear inequality looks exactly like a linear equation, with the inequality sign replacing the equality sign. Linear inequalities are the expressions where any two values compared by the inequality symbols such as $ ' < ',' > ',' \leqslant 'or' \geqslant '. $