Question

How do you solve $5x + 7 = 10$?

Answer 1

Hint: The given equation is a linear equation in one variable $x$. A linear equation is an equation where the degree or highest power of the variable is 1. The general form of a linear equation in one variable is given by $ax + b = 0$ where $x$ is the only variable. Solving the equation means finding the value of $x$ for which the equality holds true for the given equation.

Complete step-by-step solution:
The given equation $5x + 7 = 10$ is a linear equation in one variable $x$.
For solving the equation we have to find the value of $x$ for which the equality holds true, i.e., LHS=RHS.
We first shift all the terms to the LHS such that we have only the term $0$ in the RHS.
Since subtracting the same number from both sides would not disturb the equation, we subtract both sides by $10$, we get,
$
   \Rightarrow 5x + 7 - 10 = 10 - 10 \\
   \Rightarrow 5x - 3 = 0 \\
 $
Now we try to write the LHS in terms of the variable $x$ in its simplest form and shift all other terms to the RHS.
Since, adding the same number would not disturb the equation, we add $3$ on both sides,
$
   \Rightarrow 5x - 3 + 3 = 0 + 3 \\
   \Rightarrow 5x = 3 \\
 $
Then we divide by $5$ on both sides, we get,
\[
   \Rightarrow \dfrac{{5x}}{5} = \dfrac{3}{5} \\
   \Rightarrow x = \dfrac{3}{5} \\
 \]
Thus, we get the value of $x = \dfrac{3}{5}$ as the solution for the given equation.

Note: For a linear equation we get only one value of $x$ as the solution. We can add, subtract, multiply or divide both sides of an equation by same number and this does not disturb the equation. We can check whether our solution is correct or not by putting the value of $x$ in the original given equation. If LHS = RHS, the answer is said to be correct.