Solve for y (x+y)/8=M

The problem presented is a simple algebraic equation where two variables, x and y, are summed together and then divided by 8, resulting in the value M. To solve the equation, you would need to perform algebraic manipulations in order to isolate y on one side of the equation. The goal of the problem is to express y in terms of x and M, ultimately finding the value of y based on given values for x and M.

$\frac{x + y}{8} = M$

Answer

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Solution:

Step 1:

Multiply the entire equation by $8$ to eliminate the fraction.

$8 \times \frac{x + y}{8} = 8 \times M$

Step 2:

Simplify the equation by removing the common factor.

Step 2.1:

Identify and remove the common factor of $8$ .

Step 2.1.1:

Eliminate the $8$ in the numerator and denominator.

$\frac{8 (x + y)}{8} = 8 M$

Step 2.1.2:

State the simplified equation.

$x + y = 8 M$

Step 3:

Isolate $y$ by subtracting $x$ from both sides.

$y = 8 M - x$

Knowledge Notes:

The problem given is a basic algebraic equation where we are asked to solve for the variable $y$ . The equation is in the form of a fraction, which we need to manipulate to isolate $y$ . Here are the relevant knowledge points and detailed explanations:

Multiplication by the reciprocal: When we have a fraction equal to a number, we can multiply both sides of the equation by the reciprocal of the fraction's denominator to eliminate the fraction. In this case, multiplying both sides by $8$ cancels out the denominator.
Simplification: After multiplying, we simplify the equation by canceling out common factors. This is based on the property that a number divided by itself is $1$ .
Isolating the variable: To solve for a specific variable, we perform operations that will get the variable by itself on one side of the equation. This often involves adding, subtracting, multiplying, or dividing both sides of the equation by the same number. In this case, we subtract $x$ from both sides to isolate $y$ .
Equation solving: The process of solving an equation involves finding the value(s) of the variable(s) that make the equation true. In this problem, we are finding the value of $y$ in terms of $x$ and $M$ .
Algebraic operations: The steps involve using basic algebraic operations such as multiplication, division, addition, and subtraction. These operations are the foundation of solving equations and are used to manipulate the equation into a more manageable form.

By understanding and applying these concepts, we can solve a wide range of algebraic equations systematically.