Solve for m 4m-3+35=180

Solution:

Step 1:

Combine like terms on the left side of the equation.

$4m + (-3 + 35) = 180$ $4m + 32 = 180$

Step 2:

Isolate the variable $m$ by moving the constant term to the opposite side.

Step 2.1:

Subtract $32$ from both sides to get $m$ by itself.

$4m = 180 - 32$

Step 2.2:

Calculate the difference on the right side.

$4m = 148$ $4m = 148$

Step 3:

Find the value of $m$ by dividing both sides of the equation by the coefficient of $m$.

Step 3.1:

Divide the equation by $4$ to solve for $m$.

$\frac{4m}{4} = \frac{148}{4}$

Step 3.2:

Reduce the left side to $m$.

Step 3.2.1:

Eliminate the common factor of $4$.

$m = \frac{\cancel{4}m}{\cancel{4}} = \frac{148}{4}$

Step 3.2.1.1:

Recognize that $m$ divided by $1$ remains $m$.

$m = \frac{148}{4}$ $m = \frac{148}{4}$ $m = \frac{148}{4}$

Step 3.3:

Compute the division on the right side to find the value of $m$.

$m = 37$ $m = 37$ $m = 37$

Knowledge Notes:

The problem-solving process involves solving a linear equation in one variable. Here are the relevant knowledge points:

1. Combining Like Terms: This refers to the process of adding or subtracting terms that have the same variable raised to the same power. In this case, we combined the constant terms $-3$ and $35$.

2. Isolating the Variable: This is a technique used to solve for the unknown variable by getting it alone on one side of the equation. This typically involves adding, subtracting, multiplying, or dividing both sides of the equation by the same number.

3. Inverse Operations: These are operations that undo each other, such as addition and subtraction or multiplication and division. In this problem, we used subtraction to undo addition and division to undo multiplication.

4. Simplification: This involves reducing an expression to its simplest form. For example, dividing both sides of an equation by the same non-zero number simplifies the equation.

5. Equation Solving: The process of finding the value(s) of the variable(s) that satisfy the equation. In this case, we found the value of $m$ that satisfies the equation $4m - 3 + 35 = 180$.

6. Arithmetic Operations: Basic operations such as addition, subtraction, multiplication, and division are used throughout the problem-solving process.

In solving linear equations, it is important to perform the same operation on both sides of the equation to maintain equality. The goal is to isolate the variable on one side to find its value.