91Ó°ÊÓ

When you solve a linear equation, it's important to ensure that your solution is correct. This process is called verifying the solution. Verification involves substituting the solution back into the original equation and checking if both sides are equal. For example, when you find that \(x = -5\) from the equation \(5x = -25\), you substitute \(-5\) for \(x\) back into the equation, yielding \(5(-5) = -25\). If the left side equals the right side of the equation, as it does here with \(-25 = -25\), you've correctly solved the equation.

Verify each solution to avoid mistakes. Missteps in algebra are common, and verification helps catch errors. This habit also builds confidence in your solutions.

• Substitute the solution back into the original equation.
• Simplify both sides to check equality.

If they match, your solution is verified!

To solve equations, isolating the variable is often the first major step. Isolation means you rearrange the equation so the variable stands alone on one side. This allows you to solve for its value directly.

Consider the equation \(5x = -25\). Our goal is to make \(x\) the subject. By dividing both sides of the equation by 5, you are left with \(x\) on one side:

• Divide each side by 5 to cancel the coefficient of 5 from \(x\).
• This results in \(x = -5\).

Isolation of variables simplifies complex equations, making them easier to solve.

Keep in mind that what you do to one side of the equation, you must do to the other. This maintains equality and helps in accurately isolating the variable.

Division is a key operation used to solve equations, especially when dealing with coefficients attached to variables. When you have an equation like \(5x = -25\), you need to use division to isolate \(x\).

Why division? In the equation, \(5\) is a coefficient of \(x\). To detach \(x\) from its coefficient, you divide both sides by this number. This leaves you with \(x = -25 \div 5\).

• Perform the division on one side as well as the other.
• Here, dividing \(-25\) by 5 results in \(-5\).

Using division helps simplify equations to a form where solutions are evident.

Remember to apply the division on both sides to maintain the balance of the equation. This step is crucial for ensuring that your manipulation of the equation doesn't alter its equality.