Inverse order of operations for solving an equation for a specific variable:

Answer 1

To solve an equation for a specific variable, you'll often use the inverse order of operations. The basic idea is to reverse the operations applied to the variable you are isolating. Here’s a step-by-step outline of how to do this:

1. Identify the Variable: Determine which variable you want to solve for.

2. Rewrite the Equation if Necessary: Make sure the equation is in a form that can be manipulated.

3. Undo Addition/Subtraction: If the variable is being added or subtracted, do the opposite operation to both sides of the equation (i.e., if the variable has a constant added to it, subtract that constant from both sides).

   • If the equation is \(x + b = c\), subtract \(b\) from both sides to get \(x = c - b\).

4. Undo Multiplication/Division: If the variable is multiplied or divided by a number, perform the opposite operation.

   • If the equation is \(ax = b\), divide both sides by \(a\) to get \(x = \frac{b}{a}\).
   • If the equation is \(\frac{x}{c} = d\), multiply both sides by \(c\) to get \(x = dc\).

5. Undo Exponentiation/Roots: If the variable is raised to a power, use the inverse operation (taking roots) to isolate it.

   • If \(x^n = c\), take the \(n\)-th root of both sides to get \(x = \sqrt[n]{c}\).

6. Evaluate Logarithmic Operations: If the variable is in a logarithmic form, exponentiate both sides to isolate the variable.

   • If \(\log_b(x) = c\), then \(x = b^c\).

7. Rearrange terms: After isolating the variable, make sure your final equation is clean and clearly shows the variable by itself.

By following this reverse order of operations, you can isolate and solve for the specific variable you're interested in. Remember to perform the same operation on both sides of the equation to maintain equality!

Answer 2

bro just explain it in one-two sentence

Answer 3

To solve an equation for a specific variable, reverse the order of operations by undoing addition/subtraction first, then multiplication/division, followed by exponentiation/roots, until the variable is isolated on one side of the equation. Always apply the same operation to both sides to maintain equality.

Answer 4

Operations and their inverse operations:

Answer 5

Here are common mathematical operations along with their inverse operations:

1. Addition

   • Inverse: Subtraction

2. Subtraction

   • Inverse: Addition

3. Multiplication

   • Inverse: Division

4. Division

   • Inverse: Multiplication

5. Exponentiation (raising to a power)

   • Inverse: Taking the root (e.g., square root, cube root)

6. Taking the root

   • Inverse: Exponentiation (raising to the corresponding power)

7. Logarithm (log base b)

   • Inverse: Exponentiation (base \( b \) raised to the result)

By using these inverse operations, you can effectively isolate variables and solve equations.

Answer 6

one-two sentences

Answer 7

The inverse operations are: addition and subtraction, multiplication and division, exponentiation and taking roots, and logarithms and exponentiation. Each operation can be undone by applying its corresponding inverse to maintain equality in equations.