Question

question
complete the sentence based on the equation shown below.
$6x + 7 = hx + 7$
answer attempt 1 out of 2
this equation will have one solution when $h = \square$ because you get one solution when you have \quad number of xs on either side of the equation and \quad.

Explanation:

Step1: Rearrange the equation

Subtract 7 from both sides:
$6x + 7 - 7 = hx + 7 - 7$
Simplify to get: $6x = hx$

Step2: Analyze solution conditions

For one solution, the coefficients of $x$ must differ. Rearrange: $6x - hx = 0$ → $x(6 - h) = 0$. If $6 - h
eq 0$, i.e., $h
eq 6$, the only solution is $x=0$. If $h=6$, the equation becomes $0=0$, which has infinitely many solutions.

Step3: Fill in the blanks

The equation has one solution when $h$ is any value except 6, because this means there is a different number of $x$'s on either side, leading to exactly one solution for $x$.

Answer:

This equation will have one solution when $h = \boldsymbol{\text{any number except 6}}$ because you get one solution when you have a different number of x's on either side of the equation and the constant terms are equal.