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Understanding how to translate word problems into mathematical equations is the first and crucial step in solving them. In this exercise, the phrase 'Nine more than x is equal to 52' needs to be transformed into an equation. The phrase 'Nine more than' implies addition, and 'is equal to' suggests an equality sign. So, 'Nine more than x' becomes 'x + 9', and 'is equal to 52' translates to '= 52'.
Combining these parts, the equation becomes:

x + 9 = 52

If you can correctly translate the word problem into this equation, you're already halfway through solving it. Practice translating different phrases you come across in other problems to become more proficient.

Once the equation is set up, the next goal is to isolate the variable. In this example, you want to isolate x in the equation:

x + 9 = 52

To isolate the variable, you need to undo the addition of 9. You can do this by performing the opposite operation, which is subtraction. Subtract 9 from both sides of the equation:

x + 9 - 9 = 52 - 9

This simplifies to:

x = 43

By subtracting 9 from both sides, we've effectively isolated x, making it easy to see that x equals 43. Isolating variables is a key step in solving any equation, so always look for ways to isolate your variable by performing inverse operations.

The final step involves simplifying the equation to solve for the variable. After isolating the variable, you often end up with simple arithmetic. In the given example, once you isolate x, you perform a straightforward subtraction:

Starting with:

x = 52 - 9

Subtract 9 from 52, which simplifies to:

x = 43

This is your final answer. Simplifying equations typically involves basic arithmetic operations like addition, subtraction, multiplication, or division. While it seems straightforward, it's critical to ensure you perform these operations correctly to get the accurate value for your variable.
If you consistently practice these steps—translating problems, isolating variables, and simplifying equations—you'll become more adept at solving a wide range of algebraic equations.