Question

How do you solve $5x-15=8x-8$ ?

Answer 1

Hint: While solving such questions which include only one variable, collect all the terms with the variables on one side of the equation and the rest constant terms on the other side of the equation. After rearranging the terms, solve the equation for the variable to get its value.

Complete step by step solution:
Given the equation:
$5x-15=8x-8$, where $x$ is the variable for which we have to solve the equation.
Begin simplifying the equation by bringing all the terms with the variable in them to the Left-hand side of the equation and transposing all the constant terms to the Right-hand side of the equation.
$\Rightarrow 5x-8x=15-8$
Now add or subtract the like terms based on the signs accordingly to further simplify the above expression,
$\Rightarrow -3x=7$
Now to find the value of the variable $x$, divide both the sides of the above equation by$-3$,
$\Rightarrow \dfrac{-3x}{-3}=\dfrac{7}{-3}$
Linear equations can be defined as equations of the first order. The general form of a linear equation in one variable can be given as $ax+b=0$ , where $a$ is the coefficient of $x$ and $b$ is the constant.
The solutions of linear equations give values, which if substituted back in the equation makes the equation true. The linear equation $ax+b=0$ , has a unique solution which can be given by $x=\dfrac{-b}{a}$, provided$a\ne 0$.
Cancel the like terms from the denominator and numerator and take any negative sign in the denominator to the numerator,
$\Rightarrow \dfrac{-3x}{-3}=\dfrac{-7}{3}$
Therefore, after solving and simplifying the given expression in the question, that is, $5x-15=8x-8$ we get the value of the variable $x$ as $x=\dfrac{-7}{3}$.

Note: Remember to be careful while opening the parenthesis and dealing with signs while transposing terms from one side of the equation to the other side. Another method for subtracting the terms with $x$ is by taking the common factor i.e., variable $x$ common and subtracting the numbers in the bracket. If one wants to check the accuracy of the solution, one can substitute the obtained value in the given equation and check if it satisfies the equation.