Question

How do you simplify $-5\left( x-7 \right)$?

Answer 1

Hint: We multiply the coefficients of the given term of $\left( x-7 \right)$ with $-5$. The sign of the coefficient’s changes. We place an arbitrary value for x and verify the result of the equation.
The main change is the change of sign from positive to negative and negative to positive and the multiplication with 5.

Complete step by step answer:
The given equation $-5\left( x-7 \right)$ is a linear equation of x. We need to simplify for the negative sign that is present in front of the term $-5$.
We know that the use of negative signs for a term changes its value in the opposite direction. This means the use of a negative sign for a positive value changes it to a negative value. Also use of a negative sign for a negative value changes it to a positive value.
The trick is multiplying with $-1$ and then with 5.
We can express the signs in this way $\left( - \right)\times \left( + \right)=\left( - \right)$ and $\left( - \right)\times \left( - \right)=\left( + \right)$.
The individual terms in $\left( x-7 \right)$ are positive and negative respectively.
$x$ is positive and $\left( -7 \right)$ is negative.
Multiplying them with $-5$ gives $\left( -5 \right)\times \left( x \right)=-5x$ and $\left( -5 \right)\times \left( -7 \right)=35$ respectively.
Therefore, we have the final solution as $-5\left( x-7 \right)=-5x+35$.
Now we verify the solution by putting a value for x. let’s take $x=2$.
Therefore, the left-hand side of the equation becomes $-5\left( 2-7 \right)=-5\left( -5 \right)=25$.
The right-hand side of the equation is $-5x+35=-5\times 2+35=-10+35=25$.
Thus, verified the equation $-5\left( x-7 \right)=-5x+35$.

Note: The sign of the coefficient’s changes. The value for the variable is changed by the multiplication of 5. The process of multiplication and division both work similarly. In case of division, we divide with $-5$, which is similar to multiplying with $-5$ and then divide by 5.