Chapter 8.2, Problem 22GP

To determine

The solution of the equation $5m+4-7m=10$ , and check the solution.

Answer to Problem 22GP

  $m=-3$

Explanation of Solution

Given:

The equation, $5m+4-7m=10$ .

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to solve the given equation $5m+4-7m=10$ for the unknown variable, isolate the variable term m on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate m on left side, first combining both the m terms and then subtract 4 from both sides and then divide both sides by -2 and then simplify further as shown below,

  $\begin{array}{l}5m+4-7m=10\\ -2m+4=10\\ -2m+4-4=10-4\\ -2m=6\\ \frac{-2m}{-2}=\frac{6}{-2}\\ m=-3\end{array}$

Thus, the solution of the given equation is $m=-3$ .

Now, to check the solution, substitute $m=-3$ in the given equation and check whether the values on both sides of equal sign is same or no. So, it gives

  $\begin{array}{l}5m+4-7m=10\\ 5\left(-3\right)+4-7\left(-3\right)=10\\ -15+4+21=10\\ 10=10\text{True Statement}\end{array}$

Since, the left hand side and right hand side are equal, so the solution is correct.