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Solve the equation using the zero-product property.
[tex]\[ (x-8)(5x-6)=0 \][/tex]

A. [tex]\( x = -1 \)[/tex] or [tex]\( x = 5 \)[/tex]
B. [tex]\( x = 8 \)[/tex] or [tex]\( x = 1 \frac{1}{5} \)[/tex]
C. [tex]\( x = 8 \)[/tex] or [tex]\( x = -1 \frac{1}{5} \)[/tex]
D. [tex]\( x = -8 \)[/tex] or [tex]\( x = 1 \frac{1}{5} \)[/tex]

Sagot :

GinnyAnsweridn
To solve the equation [tex]\((x-8)(5x-6)=0\)[/tex] using the zero-product property, let's go through it step-by-step.

The zero-product property states that if the product of two factors is zero, then at least one of the factors must be zero.

So, we set each factor in [tex]\((x-8)(5x-6)=0\)[/tex] to zero and solve for [tex]\(x\)[/tex].

Step 1: Set the first factor equal to zero and solve for [tex]\(x\)[/tex]:

[tex]\[ x - 8 = 0 \][/tex]

To solve this, add 8 to both sides:

[tex]\[ x = 8 \][/tex]

So, one solution is:

[tex]\[ x = 8 \][/tex]

Step 2: Set the second factor equal to zero and solve for [tex]\(x\)[/tex]:

[tex]\[ 5x - 6 = 0 \][/tex]

To solve this, add 6 to both sides:

[tex]\[ 5x = 6 \][/tex]

Now, divide both sides by 5:

[tex]\[ x = \frac{6}{5} \][/tex]

So, the second solution is:

[tex]\[ x = \frac{6}{5} \][/tex]

We can write [tex]\(\frac{6}{5}\)[/tex] as a mixed number:

[tex]\[ x = 1 \frac{1}{5} \][/tex]

Conclusion:
The solutions to the equation [tex]\((x-8)(5x-6)=0\)[/tex] are:
[tex]\[ x = 8 \][/tex]
and
[tex]\[ x = 1 \frac{1}{5} \][/tex]

Therefore, the correct answer is:
[tex]\[ x = 8 \text{ or } x= 1 \frac{1}{5} \][/tex]
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