To determine whether [tex]\(-7x + 2 - 3x + 7 = 0\)[/tex] is an expression or an equation, let’s analyze its components and structure step by step.
1. Understand the Components:
- The term [tex]\(-7x\)[/tex] represents a linear term with the variable [tex]\(x\)[/tex].
- The term [tex]\(2\)[/tex] is a constant.
- The term [tex]\(-3x\)[/tex] represents another linear term with the variable [tex]\(x\)[/tex].
- The term [tex]\(7\)[/tex] is another constant.
- The expression on the right-hand side is [tex]\(0\)[/tex], which is a constant.
2. Combine Like Terms:
- First, combine the like terms involving [tex]\(x\)[/tex]: [tex]\(-7x - 3x = -10x\)[/tex].
- Next, combine the constant terms: [tex]\(2 + 7 = 9\)[/tex].
- Thus, the given statement can be simplified to [tex]\(-10x + 9 = 0\)[/tex].
3. Analyze the Structure:
- Notice the equal sign [tex]\(=\)[/tex]. This sign indicates equality between two expressions.
- On the left side, we have [tex]\(-10x + 9\)[/tex].
- On the right side, we have [tex]\(0\)[/tex].
4. Definition:
- An expression is a combination of numbers, variables, and operations (such as addition and multiplication) but does not include an equal sign [tex]\(=\)[/tex].
- An equation is a statement that asserts the equality of two expressions, which means it includes an equal sign [tex]\(=\)[/tex].
Since the statement [tex]\(-10x + 9 = 0\)[/tex] includes an equal sign, it asserts the equality between the expression [tex]\(-10x + 9\)[/tex] and the constant [tex]\(0\)[/tex]. Therefore, it is an equation.
So, the given mathematical statement [tex]\(-7x + 2 - 3x + 7 = 0\)[/tex] is an equation.
