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Translating phrases from English into algebraic expressions is a fundamental skill that bridges the gap between words and mathematical equations. It's like translating a language. For example:

- The phrase

An algebraic expression is a mathematical phrase that includes numbers, variables, and operation symbols. In our exercise:

- We translated 鈥渢en less than a number鈥� into the algebraic expression 饾憶 - 10.
- Also, note that 鈥渢hree more than six times the number鈥� was translated into 6饾憶 + 3.

These expressions don't have an equal sign. They're just parts of a whole equation. When you understand how to write these expressions, you can easily handle algebra problems. Practice is key! Go through as many examples as you can to get familiar with the process.

Remember, algebraic expressions can be simplified and combined based on the math operations involved. Take it step-by-step and always keep track of the variable and constants involved.

Setting up equations is like assembling a puzzle. Each piece, which is an algebraic expression, needs to fit together to represent the given problem. Let鈥檚 look at the specific example:

- From the steps, we have 饾憶 - 10 from the phrase 鈥渢en less than a number鈥� and 6饾憶 + 3 from 鈥渢hree more than six times the number.鈥�

To set up the equation, we combine these expressions as follows:

- The phrase 鈥渋s鈥� usually signals equality in algebra. Hence, we set up the equation 饾憶 - 10 = 6饾憶 + 3.

This equation states that ten less than our number equals three more than six times our number. Remember to carefully translate each part and then combine them as shown.

Once the equation is written, you can solve it using algebraic methods. This involves isolating the variable on one side of the equation and simplifying step-by-step. Setting up equations correctly is essential in solving algebra problems accurately.