Problem 30 - Elementary Algebra Within Reach

Question

Solve the equation and check your solution. $$-11 y-44=0$$

Step-by-Step Solution

Answer

The solution is y = -4

Step 1: Add 44 to Both Sides

First, we need to get rid of the -44 on the left side of the equation. We will do this by adding 44 to both sides of the equation, which gives us -11y = 44.

Step 2: Divide by -11

Next, we need to isolate the variable y. We will do this by dividing both sides of the equation by -11, which gives us y = -4.

Step 3: Check the Solution

The final step is to check the solution. We do this by substituting y in the original equation with our found value, -4. By substituting we get -11*-4 - 44 = 0. Now we simplify the expression which gives us 0=0. This confirms that y = -4 is the correct solution.

Key Concepts

Checking Solutions

Checking your solution in an equation is like double-checking your answers. It ensures that the solution you found is not just mathematically correct, but also practically valid. Imagine finding a treasure map; you'd want to verify each step to ensure you're on the right path.
To check the solution for the equation \(-11y - 44 = 0\), once you've found \(y = -4\), you substitute \(-4\) back into the original equation.
Here's how the check works:

• Start with the original equation: \(-11y - 44 = 0\).
• Substitute \(y\) with \(-4\): \(-11(-4) - 44 = 0\).
• Simplify: \(44 - 44 = 0\), which gives you \(0 = 0\).

Everything balances, which means \(y = -4\) is indeed the correct solution! This step ensures that any possible calculation errors are caught, giving you better confidence in your results.

Step-by-Step Solutions

Tackling equations in a step-by-step manner can make the process less intimidating and more logical. Think of it as following a recipe to bake a cake: each ingredient needs attention.
Here's a look into solving the equation \(-11y - 44 = 0\) using a structured approach:

• Identify the equation: Notice how it's structured and aim to simplify.
• Add 44 to both sides: To remove \(-44\), perform the same operation on both sides, resulting in \(-11y = 44\).
• Solve for \(y\): Divide each side by \(-11\) to isolate \(y\), resulting in \(y = -4\).

Each step is like a rung on a ladder that leads you to the solution. It's important to maintain balance in your equation by performing the same operations on both sides.

Isolating Variables

Isolating the variable is crucial in solving equations and is akin to peeling an onion until you reveal the core. The goal is to have the variable on one side of the equation, all by itself.
In our example \(-11y - 44 = 0\), your task is to get \(y\) on one side:

• Add \(44\) to undo \(-44\), simplifying it to \(-11y = 44\).
• Next, solve for \(y\) by dividing both sides by \(-11\). This eliminates the coefficient \(-11\), leaving \(y = -4\).

The process of isolating the variable ensures clarity and accuracy in determining the true value the variable holds. With practice, this process becomes more intuitive and quicker.