Question

Five less than twice a number is equal to seven times the number. Find the number.

Answer 1

Let the number be $x,$ then five less than twice of $x$ is equal to seven times of $x.$
$\Rightarrow 2x-5=7x$

Step 1: Add 5 to both sides of the equation to eliminate 5 on the left side of the equation.
$\Rightarrow 2x-5+5=7x+5\Rightarrow 2x=7x+5$

Step 2: Subtract both sides of the equation by $7x$ to eliminate $7x$ on the right side of the equation.
$\Rightarrow 2x-7x=7x+5-7x$
$\Rightarrow -5x=5$

Step 3: Now, divide both sides by -5 to eliminate -5 on the left side of the equation.
$\Rightarrow \frac{-5x}{-5}=\frac{5}{-5}\Rightarrow x=-1$

Hence, the required number is $-1.$