Question

Harrison writes an algebraic expression with four terms. The x term has a coefficient of two, and the z term has a coefficient of -1. The expression has a constant term less than zero. Which expression could he have written?

a) \(2x - y - z - 5\)

b) \(2x + y - z - 3\)

c) \(4x - 2y - z + 1\)

d) \(3x - 4y + z - 2\)

Answer 1

Harrison could have written the expressions 2x - y - z - 5 (option a) and 2x + y - z - 3 (option b) because both contain a x term with a coefficient of 2, a z term with a coefficient of -1, and a constant term less than zero.

Step-by-step explanation:

The question asks which algebraic expression Harrison could have written, given that the expression has four terms with a coefficient of two for the x term and a coefficient of -1 for the z term, and a constant term less than zero. Inspecting the provided options:

• Option a) 2x - y - z - 5 has a coefficient of 2 for the x term, a coefficient of -1 for the z term, and a constant term of -5, which is less than zero.
• Option b) 2x + y - z - 3 also meets the criteria with the same coefficients for the x and z terms and a constant term of -3.
• Option c) 4x - 2y - z + 1 does not meet the criterion for the coefficient of the x term nor the constant term.
• Option d) 3x - 4y + z - 2 does not meet the criteria for the coefficients of both x and z terms.

Thus, the expressions that Harrison could have written are option a) and option b).