Complete the sentence based on the equation shown below.

Question

minus, 5, left parenthesis, x, minus, 10, right parenthesis, equals, h, of, minus, x, plus, 8
−5(x−10)=
h(−x+8)
Answer
Attempt 1 out of 2

This equation will have one solution when h, equalsh=
because you get one solution when you have
number of x's on either side of the equation and

Answer 1

To complete the sentence based on the given equation, we need to first simplify the equation and analyze it.

Starting with the equation: \[ -5(x - 10) = h(-x + 8) \]

First, we can expand the left side: \[ -5(x - 10) = -5x + 50 \]

Now we have: \[ -5x + 50 = h(-x + 8) \]

Next, let's express \( h(-x + 8) \): \[ h(-x + 8) = -hx + 8h \]

Now, we need to find out when this equation has one solution. This happens when the coefficients of \( x \) are equal on both sides of the equation, and there is not a contradiction in the constant terms.

From our current equation:

1. The coefficient of \( x \) on the left is \(-5\).
2. The coefficient of \( x \) on the right is \(-h\).

For the equation to have one solution, the coefficients of \( x \) must be equal: \[ -5 = -h \] This simplifies to: \[ h = 5 \]

Also, we need to assess the constant term. The constant term on the left is \(50\) and on the right is \(8h\). With \(h = 5\), the constant on the right becomes: \[ 8h = 8 \times 5 = 40 \] Since \(50\) does not equal \(40\), it confirms there will be one intersection point (solution) for the lines defined by their expressions.

Thus, we can complete the sentence:

This equation will have one solution when \(h = 5\) because you get one solution when you have equal coefficients of \(x\) on either side of the equation and a consistent constant term, leading to a single point of intersection.