Question

How do you solve $-3x+4>-11$?

Answer 1

Hint: We first try to find the similarities for binary operations in between equation and inequation. We try to keep the variable and the constants separate and on opposite sides of the inequality. We subtract 4 from both sides. Then we divide the inequation by $-3$ and find the range of the variable $x$.

Complete step by step answer:
We have been given an inequality where the inequation is $-3x+4>-11$.
We need to find the solution or range for the variable $x$.
Now we try to keep the variable and the constants separate.
The binary operation of subtraction in case of inequation works in similar way to an equation.
There will be no change in the sign of the inequation.
Now we subtract 4 from the both sides of the inequation of $-3x+4>-11$.
\[\begin{align}
  & -3x+4>-11 \\
 & \Rightarrow -3x+4-4>-11-4 \\
\end{align}\]
We perform the binary operations in both cases and get
\[\begin{align}
  & -3x+4-4>-11-4 \\
 & \Rightarrow -3x>-15 \\
\end{align}\]
Now we divide the inequation with $-3$ to find the solution. The sign of the inequality changes as we are dividing with negative value.
\[\begin{align}
  & \dfrac{-3x}{-3}<\dfrac{-15}{-3} \\
 & \Rightarrow x<5 \\
\end{align}\]

The solution for the equation $-3x+4>-11$ is that the value of the variable $x$ will be less than 5.

Note: We need to remember that in inequality we are never going to find a particular solution. In most of the cases we are going to find the range or interval as a solution. For our given inequality $-3x+4>-11$, we got the variable $x$ to be less than 5. It’s a range of $x$. We can express it as $x\in \left( -\infty ,5 \right)$.