Question

How do solve $13x+26<65$ ?

Answer 1

Hint: At first, we bring the $26$ term to the right hand side of the inequality by subtracting it from both sides of the inequality. The, we divide both sides of the inequality by $13$ and get the final solution in terms of another inequality.

Complete step by step solution:
The given inequality that we have at our disposal is
$13x+26<65$
Now, we know that solving an inequality is quite similar to solving an equation. All the operations remain the same except that in inequality, if we multiply or divide both sides by a negative number, or take reciprocals, we need to reverse the inequality sign. So, keeping these in mind, we start off with the solution.
At first, we subtract $26$ from both sides of the inequality. The inequality thus after rewriting becomes,
$\Rightarrow 13x+26-26<65-26$
The above inequality upon simplification gives,
$\Rightarrow 13x<39$
Now, we divide both sides of the inequality by $13$ and the inequality thus after rewriting becomes,
$\Rightarrow \dfrac{13x}{13}<\dfrac{39}{13}$
The above inequality simplification gives,
$\Rightarrow x<3$
This means all values of $x$ smaller than $3$ satisfy the given inequality.
Therefore, we can conclude that the solution of the given inequality is $x<3$ .

Note:
The only thing that students should remember while solving inequalities is the negative signs and the reciprocals. So, it's better if we cross check our solution by putting a random value of the solution in the given inequality. Also, all the terms in the inequality being multiples of $13$ , we can divide by $13$ on both sides at first and then proceed. In this way, the expression gets simpler and less prone to mistakes.