What is the simplest form of the expression $(-11.7 y-3.3 x)+1.2 x+(5.2 y+x)?
Answer (2)
Group the y terms: − 11.7 y + 5.2 y = − 6.5 y .
Group the x terms: − 3.3 x + 1.2 x + x = − 1.1 x .
Combine the simplified y and x terms.
The simplified expression is − 6.5 y − 1.1 x .
Explanation
Understanding the Expression We are asked to simplify the expression ( − 11.7 y − 3.3 x ) + 1.2 x + ( 5.2 y + x ) . This involves combining like terms, meaning we group the y terms together and the x terms together.
Grouping y Terms First, let's identify and group the y terms: − 11.7 y and 5.2 y . Combining these gives us: − 11.7 y + 5.2 y = ( − 11.7 + 5.2 ) y
Calculating y Coefficient Now, let's calculate the coefficient for the y terms: − 11.7 + 5.2 = − 6.5 So, the combined y term is − 6.5 y .
Grouping x Terms Next, let's identify and group the x terms: − 3.3 x , 1.2 x , and x . Combining these gives us: − 3.3 x + 1.2 x + x = ( − 3.3 + 1.2 + 1 ) x
Calculating x Coefficient Now, let's calculate the coefficient for the x terms: − 3.3 + 1.2 + 1 = − 1.1 So, the combined x term is − 1.1 x .
Simplified Expression Finally, we combine the simplified y and x terms to get the simplified expression: − 6.5 y − 1.1 x
Examples
Simplifying algebraic expressions is a fundamental skill in mathematics with applications in various fields. For instance, in physics, you might need to simplify an expression representing the forces acting on an object. Suppose the forces in the x and y directions are given by expressions similar to the one we simplified. By combining like terms, you can determine the net force acting on the object more easily. This skill is also crucial in computer science for optimizing code and in economics for simplifying cost and revenue functions.
To simplify the expression ( − 11.7 y − 3.3 x ) + 1.2 x + ( 5.2 y + x ) , we group the y terms and x terms separately. The combined y term is − 6.5 y and the combined x term is − 1.1 x . Therefore, the simplest form is − 6.5 y − 1.1 x .
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