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Complete the sentence based on the equation shown below.

[tex]\[ h(-2x+2) = -8(x-8) \][/tex]

This equation will have one solution when [tex]\( h = \square \)[/tex] because you get one solution when you have [tex]\(\square\)[/tex] number of [tex]\(x\)[/tex] 's on either side of the equation.

Sagot :

GinnyAnsweridn
To find the value of [tex]\( h \)[/tex] that will ensure the equation:

[tex]\[ h(-2x + 2) = -8(x - 8) \][/tex]

has a single unique solution, we need to ensure that the coefficient of [tex]\( x \)[/tex] on both sides of the equation are equal.

1. Start by simplifying both sides of the equation.

Left side:
[tex]\[ h(-2x + 2) = h(-2x) + h(2) = -2hx + 2h \][/tex]

Right side:
[tex]\[ -8(x - 8) = -8x + 64 \][/tex]

2. For the equation to have a single unique solution, the coefficients of [tex]\( x \)[/tex] on both sides need to be the same.

Compare the coefficients of [tex]\( x \)[/tex]:
[tex]\[ -2h = -8 \][/tex]

3. Solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{-8}{-2} = 4 \][/tex]

We also ensure that the constant terms (terms without [tex]\( x \)[/tex]) do not affect the number of solutions. The equation is balanced once the [tex]\( x \)[/tex] coefficients are aligned.

Thus, the number of [tex]\( x \)[/tex]'s on either side of the equation is the same (specifically, one on each side).

So the completed sentence should read:
This equation will have one solution when [tex]\( h = 4 \)[/tex] because you get one solution when you have 1 number of [tex]\( x \)[/tex]'s on either side of the equation.
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