Algebra practice question

Answer: B. -1

The left side simplifies to 12x + 30 - 4x = 8x + 30. The right side simplifies to 3kx - 6 + 11x = (3k + 11)x - 6. An equation of the form ax + b = cx + d has no solution exactly when a = c and b is not equal to d. Setting 3k + 11 = 8 gives 3k = -3, so k = -1; the constants 30 and -6 differ, so there is indeed no solution. (A) -3 results from failing to distribute the 3 to the kx term, solving k + 11 = 8. (C) 1 results from a sign error when solving 3k = -3, treating it as 3k = 3. (D) 8/3 results from ignoring the separate 11x term on the right and solving 3k = 8.

Why the other answers are wrong

A. -3

You solved k + 11 = 8, which means the 3 in 3(kx - 2) never got distributed to the kx term. Distributing gives 3kx, so the coefficient equation is 3k + 11 = 8.

C. 1

Your setup was right, but 3k = -3 gives k = -1, not 1 — check the sign when you divide.

D. 8/3

You set 3k = 8, ignoring the separate 11x on the right side. The full right-side coefficient of x is 3k + 11, and that must equal 8.

More Algebra questions

• Very hard
  For what value of c does the system 3x − 2y = 8 and 9x + cy = 5 have no solution?
• Very hard
  In the system 5x + 4y = 32 and 3x − 2y = 6, what is the value of 8x + 2y?
• Very hard
  The solution set of the inequality |ax − b| ≤ 6, where a and b are constants and a > 0, is 3 ≤ x ≤ 9. What is …
• Very hard
  The function f is linear, and for every value of x, f(x + 2) − f(x) = 6. If f(5) = 4, what is the value of f(0…
• Very hard
  In the system of equations 2x + 3y = 12 and 5x − 2y = k, where k is a constant, the solution (x, y) satisfies …
• Very hard
  In the xy-plane, the system of equations kx + 6y = 12 and 2x + (k − 1)y = 6, where k is a constant, has infini…