Question

How do you solve $5x + 7 > 17$?

Answer 1

Hint: The given inequation is a linear inequation in one variable. An inequation is different from an equation inasmuch as an inequation compares two expressions holding non-equality rather than holding equality of expressions. Solution of given inequation here may give a range of values for $x$ and not just one single value as result.

Complete step-by-step solution:
The given inequation is $5x + 7 > 17$.
We have to find the values of $x$ for which the given inequation holds true.
First we try to simplify the inequation such that the RHS contains no other term than $0$. For this, we subtract $17$ from both sides of the inequation. We get:
\[
   \Rightarrow 5x + 7 - 17 > 17 - 17 \\
   \Rightarrow 5x + 10 > 0 \\
 \]
Now, to get the value of $x$ we have to get the variable $x$ in its simplest form in the LHS and all other terms in the RHS. Since it is a linear inequation, the simplest form of the variable $x$ would be $x$ itself.
Now, by subtracting \[10\] from both the sides of the equation, we get:
$
   \Rightarrow 5x + 10 - 10 > 0 - 10 \\
   \Rightarrow 5x + 0 > - 10 \\
   \Rightarrow 5x > - 10 \\
 $
Now, we divide both sides by $5$ to get:
$
   \Rightarrow \dfrac{{5x}}{5} > \dfrac{{ - 10}}{5} \\
   \Rightarrow x > - 2 \\
 $
Thus, the solution that we get is \[x > - 2\], i.e. for any number greater than $ - 2$ as the value of $x$ the inequality holds true in the given inequation.

Note: Even in an inequation, adding a number to both sides and subtracting a number from both sides would not disturb the inequation. Also, multiplying or dividing by a positive number both sides of an inequation would not disturb the inequation. However, when multiplying or dividing by a negative number the sign of inequality reverses, i.e. greater than (>) becomes less than (<) and vice-versa. For solution of an inequation we get a range of values as a result.