91Ó°ÊÓ

When simplifying algebraic expressions, the first step usually involves combining like terms. Like terms are terms in an expression that have the same variable raised to the same power. For example, in the expression \(-\frac{5}{6}+8x+\frac{1}{6}x-7-\frac{7}{6}\), the like terms are the constants \(-\frac{5}{6}\), \(-7\), and \(-\frac{7}{6}\), as well as the variable terms \(8x\) and \(\frac{1}{6}x\).

Grouping these like terms together helps you simplify the expression. It's like sorting socks: you put the ones with the same color and pattern together. In math, constants go with constants, and terms with the variable \(x\) go with other terms with the variable \(x\). This grouping makes it easier to add or subtract the terms later.

Simplifying fractions is crucial when working with algebraic expressions, especially when you have to combine fractions with different denominators. Consider the constants in the given expression: \(-\frac{5}{6} - 7 - \frac{7}{6}\).

To combine these, you need a common denominator. The denominator in this case is 6. So, convert each constant term to have the same denominator: \(-7\) becomes \(-\frac{42}{6}\).

Combining them involves straightforward addition and subtraction:

• \(-\frac{5}{6} - \frac{42}{6} - \frac{7}{6}\)
• Combine the fractions: \-\frac{54}{6} = -9\.

Simplifying fractions transforms them into a form that makes combining terms easy and less error-prone.

Variable terms and constants are the two building blocks of algebraic expressions. Constants are the fixed numbers in the expression (like \(-7\)), while variable terms include variables (like \(x\)).

To simplify our expression, the next step involves the variable terms \(8x + \frac{1}{6}x\). Convert \(8x\) to have a common denominator with \(\frac{1}{6}x\): \(8x = \frac{48}{6}x\).

Now, add them together to get: \(\frac{48}{6}x + \frac{1}{6}x = \frac{49}{6}x\).

This leaves us with:

• Simplified constants: \-9\
• Simplified variable terms: \frac{49}{6}x\

Combining them, the finalized simplified expression is \-9\(\frac{49}{6}x\).