Question

How do you solve it $17 = - 13 - 8x$ ?

Answer 1

Hint: At first, we have to write this equation in the form where the constant part will be on one side and the variable part will be on another side. Then we have to add between the two constant terms. Then we will get a simplified form of the equation. Then finally by simplification, we will get the value of $x$ .

Complete step-by-step solution:
We have;
$17 = - 13 - 8x$
At first, we will add $\;13$ on both sides and get;
$\Rightarrow 17 + 13 = - 13 - 8x + 13$
$\Rightarrow 30 = - 8x$
Now we will divide both sides with $- 8$ and get;
$\Rightarrow - \dfrac{{30}}{8} = x$
$- \dfrac{{30}}{8}$ can be written as $- \dfrac{{5 \times 3 \times 2}}{{4 \times 2}}$ .
So we will get;
$\Rightarrow x = - \dfrac{{5 \times 3 \times 2}}{{4 \times 2}}$
As we can see $2$ is common in numerator and denominator, we will cut out $2$ both from numerator and denominator.
Hence we will get;
$\Rightarrow x = - \dfrac{{5 \times 3}}{4}$
Now we will multiply the terms of numerator and get;
$\Rightarrow x = - \dfrac{{15}}{4}$
So, the simplified form of the given equation is $x = - \dfrac{{15}}{4}$ .
We can transform the value of $x$ in decimal representation from the rational form.

The value of x is $- 3.75$.

Note: In this question, we have been given $17 = - 13 - 8x$ . This is in the form $ax + b = 0$ . This type of equation is called a linear equation. In this equation, $x$ is called variable and $a$ is called the coefficient of the variable. Here $b$ is called the constant part. Generally, a linear equation is the simplest form of a system of polynomial equations. The polynomial equations are ${a_m}{x^m} + {a_{m - 1}}{x^{m - 1}} + ......... + {a_2}{x^2} + {a_1}x + {a_0} = 0$ ; where $m = 0,1,2...$ .