91Ó°ÊÓ

When solving linear equations, it's essential to simplify the equation first. You do that by combining like terms.
These are terms that have the same variable raised to the same power.
In the equation, we have terms with the variable ‘z’ on both sides:

• On the left side: 2z
• On the right side: -z

Start by adding ‘z’ to both sides to get all the ‘z’ terms on the same side:

\[2z - 4 + z = 23 - z + z\] By combining these terms, we simplify our equation to: \[3z - 4 = 23\] This makes it much easier to work with.
Always remember, combining like terms helps to consolidate variables and constants. This step is vital for simplifying the equation effectively.

After combining like terms, the next step is isolating the variable. This means getting the variable on one side of the equation and constants on the other.
In this case, we want to isolate ‘z’.
The equation after combining like terms is:

• 3z - 4 = 23

Add 4 to both sides to move the constant term:

\[3z - 4 + 4 = 23 + 4\] Simplifying this, we get: \[3z = 27\] Now, the variable term (3z) is isolated on one side, and the constants are on the other.
Isolating the variable paves the way for us to find its value.

The final step is solving for the variable. Now that we have the equation simplified to:

• 3z = 27

We solve for ‘z’ by dividing both sides of the equation by 3:

\[\frac{3z}{3} = \frac{27}{3}\] Simplifying this, we get: \[z = 9\] And there we have it!
By performing these straightforward steps – combining like terms, isolating the variable, and solving for the variable – we solved the equation and found that z = 9.
Remember, it's always important to double-check your work to ensure accuracy.