Question

1. how many terms are in the expression below? what are the constants in the expression?

5x - 4 + 7y - 3 + 6z + 4x
a. 4 terms: constants 4 and 3
b. 6 terms: constants -4 and -3
c. 6 terms: constants 5, 7, 6, and 4
d. 4 terms: constants 5,7,6, and 4

Explanation:

Step1: Identify terms in the expression

The given expression is \(5x - 4 + 7y - 3 + 6z + 4x\). First, we combine like terms. The like terms for \(x\) are \(5x\) and \(4x\), so \(5x + 4x=9x\). The expression now is \(9x - 4 + 7y - 3 + 6z\). Now, we identify each term: \(9x\), \(-4\), \(7y\), \(-3\), \(6z\). Wait, no, originally without combining, the terms are \(5x\), \(-4\), \(7y\), \(-3\), \(6z\), \(4x\). So that's 6 terms? Wait, no, let's list them properly. The expression is \(5x + (-4) + 7y + (-3) + 6z + 4x\). So the terms are \(5x\), \(-4\), \(7y\), \(-3\), \(6z\), \(4x\). So that's 6 terms. Now, constants are terms without variables, so \(-4\) and \(-3\). Wait, but let's check the options. Option b says 6 terms, constants \(-4\) and \(-3\). Let's verify:

• Terms: \(5x\), \(-4\), \(7y\), \(-3\), \(6z\), \(4x\) → 6 terms.
• Constants: \(-4\) and \(-3\) (since they have no variables).

So option b matches.

Answer:

b. 6 terms: constants -4 and -3