To evaluate and simplify the algebraic expression [tex]\(4x + 25 - 42y\)[/tex], let's follow a step-by-step approach:
1. Identify the terms: The given expression consists of three terms: [tex]\(4x\)[/tex], [tex]\(25\)[/tex], and [tex]\(-42y\)[/tex].
2. Combining like terms: In this expression, we have two different types of terms: those involving the variables (like [tex]\(4x\)[/tex] and [tex]\(-42y\)[/tex]) and the constant term ([tex]\(25\)[/tex]). Since [tex]\(4x\)[/tex] and [tex]\(-42y\)[/tex] are different with respect to their variables, and [tex]\[25\][/tex] has only a constant value, you do not combine them further.
3. Rewriting the expression: Assemble the terms with respect to their contributions to the final expression:
- The coefficient of [tex]\(x\)[/tex] is [tex]\(4\)[/tex], and so the term involving [tex]\(x\)[/tex] remains [tex]\(4x\)[/tex].
- The constant [tex]\(25\)[/tex] stands alone as is.
- The coefficient of [tex]\(y\)[/tex] is [tex]\(-42\)[/tex], and the term involving [tex]\(y\)[/tex] remains [tex]\(-42y\)[/tex].
By arranging all terms, the expression maintains its form:
[tex]\[ 4x + 25 - 42y \][/tex]
4. Ordered arrangement: As we commonly write expressions in a standardized form, we organize it in terms of [tex]\(x\)[/tex] first, followed by [tex]\(y\)[/tex] and then the constant term if applicable.
Therefore, the simplified algebraic expression can be written as:
[tex]\[ 4x - 42y + 25 \][/tex]
This is the final simplified form of the given algebraic expression.
