Question

How do you solve $12p + 7 > 139$?

Answer 1

In order to determine the value of variable $p$ in the above inequality use the rules of transposing terms to transpose terms having $p$ on the Left-hand side and constant value terms on the Right-Hand side of the inequality. Solving like terms and dividing both sides of the inequality with the coefficient of variable $p$ will lead to your required result.

Complete step by step answer:
We are given a linear inequality in one variable $12p + 7 > 139$ and we have to solve this for the inequality variable ($p$).
$\Rightarrow 12p + 7 > 139$
Now combining like terms on both of the sides of the inequality. Terms having $p$ will on the Left-Hand side of the equation and constant terms on the right-hand side .
Let’s recall one basic property of transposing terms that on transposing any term from one side to another the sign of that term gets reversed. In our case,$+ 7$ on the left hand side will become $- 7$ on the right hand side .
After transposing terms our equation becomes
$\Rightarrow 12p > 139 - 7$
Now, solving the Right-hand side, we get
$\Rightarrow 12p > 132$
Dividing both sides by the coefficient of variable ($p$) i.e. $12$
$\Rightarrow \dfrac{{12p}}{{12}} > \dfrac{{132}}{{12}} \\\ \Rightarrow p > 11 \\\$
i.e.$(11,\infty )$, variable p is greater than 11

Therefore, the solution to the inequality $\Rightarrow 12p + 7 > 139$is$p > 11$or$(11,\infty )$.

Additional Information:
Linear Inequality: A linear equality is a mathematical expression in which two values or two expressions are compared with each other. They are compared with the inequality symbols like $< , > , \geqslant, \leqslant$. Values can be either numerical / algebraic or can be a combination of both. The inequality symbols ($< , >$) are used to express strict inequalities and on the other hand symbols $( \geqslant, \leqslant )$ are slack inequalities.

Note: 1. One must be careful while calculating the answer as calculation error may come.
2. Inequalities having symbol $( \geqslant , \leqslant )$ are slack inequalities
3. Inequalities having symbol $( > , < )$ are strict inequalities