91Ó°ÊÓ

Algebraic equations are mathematical statements that show the equality between two expressions. In these equations, we often have unknowns, which we represent using variables like 'h'. To solve the equation, we need to find the value of the variable that makes the equation true.

For example, in the equation \(\frac{h}{-13} = -65\), 'h' is the variable. We need to determine the value of 'h' such that when it is divided by -13, the result is -65. This process involves translating a real-world statement into an algebraic equation and then solving for the unknown variable.

When multiplying numbers, the signs of the numbers are crucial. The basic rules for multiplying positive and negative numbers are:

• Positive \( \times \) Positive = Positive
• Negative \( \times \) Negative = Positive
• Positive \( \times \) Negative = Negative
• Negative \( \times \) Positive = Negative

In our exercise, we have \(-65 \times -13\). Since both numbers are negative, their multiplication will result in a positive number. Therefore, \(-65 \times -13 = 845\).

It helps to remember that multiplying two negative numbers cancels out the negative signs because a negative times a negative is a positive.

Isolating the variable means getting the variable by itself on one side of the equation. This is often done through a series of inverse operations. Inverse operations are operations that reverse the effect of another operation. For example, multiplication is the inverse of division and vice versa.

In the given exercise \(\frac{h}{-13} = -65\), the goal is to isolate 'h'.
To do that, we perform the inverse operation of division. Since 'h' is divided by -13, we multiply both sides of the equation by -13 to cancel out the division. This gives us:
\ h = -65 \times -13 \
This process helps to eliminate the division and move us closer to solving for 'h'.

Isolating the variable is a critical step in solving algebraic equations. By performing inverse operations, we can manipulate the equation and find the value of the variable that satisfies the equation.