Question

How do you solve $4m+9+5m-12=42$?

Answer 1

Hint: In this question, we are given an equation in terms of variable m and we need to solve it. We need to find the value of m which satisfies this equation. For this, we will try to add or subtract or multiply or divide certain terms on both sides of the equation such that we are left with only variable m on the left side of the equation and a constant on the right side of the equation. That constant on the right side will be the required values of m which satisfies the equation.

Complete step by step answer:
Here we are given the equation in terms of variable m as: $4m+9+5m-12=42$. We need to solve it to find the value of m which satisfies this equation. For this we will use proper operation (addition/subtraction/multiplication/division) to manipulate the equation in the form as m = c where c will be any constant.
Our equation looks like $4m+9+5m-12=42$.
As we can see, there are like terms 4m and 5m on one side of the equation with additional symbols, so we can add them and get (4+5)m = 9m. So our equation reduces to $9m+9-12=42$.
We have two constant 9 and -12 on the left side let us simplify them to make one constant only. We know that 12-9 is equal to 3 but the negative sign is with 12 which is a greater term so we will have -12+9 as -3 we get $9m-3=42$.
Now we can see that, -3 is a constant and it shall be only on the right side of the equation. So for removing it from the left side of the equation lets add 3 on both sides of the equation. We get $9m-3+3=42+3$.
Let us solve the constant terms we get $9m=45$.
The equation is not in the form m = c as there exists a coefficient of m. So let us remove it. Since 9 is multiplied to m. To remove it let us divide both sides by 9 we get \[\dfrac{9m}{9}=\dfrac{45}{9}\].
9 divided by 9 gives 1 and we know 45 divided by 9 gives 5 so we get m = 5 which is of the form m = c. Therefore the value of m is equal to 5 which is the required answer.

Note:
Students should always take care of the signs while solving the equation. Make sure to use proper operation as required. They can check their answer by following way,
Putting values of m as 5 in the original equation we get, $4\left( 5 \right)+9+5\left( 5 \right)-12=42$.
Solving the left side of the equation we get,
$20+9+25-12=42\Rightarrow 29+25-12=42\Rightarrow 54-12=42\Rightarrow 42=42$.
Left hand side is equal to the right hand side of the equation. Therefore, m = 5 is the correct answer.