Complete the sentence based on the equation shown below. h, of, minus, 3, x, minus, 6, equals, minus, 12, x, minus, 36 h(−3x−6)= −12x−36 Answer This equation will have one solution when h, equals h= because you get one solution when you have a different number of x's on either side of the equation and

1 answer

This equation will have one solution when \( h = -4 \) because you get one solution when you have a different number of \( x \)'s on either side of the equation and the coefficients of \( x \) do not match in such a way that allows for infinite solutions or contradictions.

To elaborate, if you let \( h = -4 \), both sides maintain a linear relationship but will intersect at a single point based on the condition imposed by the \( h \) value. This ensures that the equation simplifies in a way to isolate \( x \) effectively leading to one unique solution.

If we re-write the equation \( h(-3x - 6) = -12x - 36 \), we can solve for \( h \):

  • Distributing \( h \): \( -3hx - 6h = -12x - 36 \).
  • Rearranging for \( x \): Set the coefficients of \( x \) on both sides equal, which gives us \( -3h = -12 \) or \( h = 4 \).

But if we find a scenario where the equation structurally allows both sides to have varying coefficients of \( x \), that justifies a unique solution. Therefore, confirming \( h = -4 \) provides the required conditions for the insights provided.

Similar Questions
  1. Complete the sentence based on the equation shown below.minus, 5, left parenthesis, x, minus, 10, right parenthesis, equals, h,
    1. answers icon 1 answer
    1. answers icon 1 answer
  2. Complete the sentence based on the equation shown below.minus, 8, left parenthesis, x, plus, 3, right parenthesis, equals, h,
    1. answers icon 1 answer
  3. Viktoriya solved an equation as shown below.5 (x minus 2) minus 3 x = 2 (x minus 3) minus 16. 5 x minus 10 minus 3 x = 2 x minus
    1. answers icon 1 answer
more similar questions