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Solving equations is the foundation of algebra. It's a process used to find the value of variables that make an equation true. Think of an equation like a balanced scale, where whatever you do to one side must be done to the other to keep it balanced. In the given problem, the equation is \(5t = 20\). Here, \(t\) is the variable we need to solve for. The equation tells us that \(5\) times some number \(t\) equals \(20\). To solve it, you want to make \(t\) "sit alone" or be isolated. This way, you'll know exactly what \(t\) is equal to. But remember, solving equations can involve different operations, such as adding, subtracting, multiplying, or dividing, depending on the structure of the equation. In this problem, we utilize the multiplication principle.

Checking solutions is an essential step in solving equations. It ensures that the value you found truly satisfies the original equation, maintaining its balance.To check your work for \(5t = 20\), you substitute the found value of \(t\) back into the equation to see if both sides are equal. In our case, if \(t = 4\), substituting back gives us: - Left side: \(5 \times 4 = 20\) - Right side: \(20\)Since both sides equate to \(20\), it confirms that the solution \(t = 4\) is correct. This step provides confidence that the solution is accurate and reliable, and it is crucial to perform this verification whenever possible.

Isolating variables involves rearranging equations to have the variable of interest on one side alone. This simplification helps in identifying the value of the variable clearly.In the problem \(5t = 20\), we need to isolate \(t\). Since \(t\) is multiplied by \(5\), we do the opposite operation, division, to both sides of the equation. By dividing both sides by \(5\), you perform: \[\frac{5t}{5} = \frac{20}{5}\]This process effectively removes the \(5\) from alongside \(t\), leading to \(t = 4\). The goal in isolating the variable is to simplify the equation to the point where the variable is by itself on one side, making it easy to see what the variable equals.