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Answer:

The algebraic sentence, “Eleven more than eight times a number is -12“, can be translated and written into an algebraic equation such as:

[tex]8x + 11 = 12[/tex]

And the solution of this equation is:  [tex]x=\frac{1}{8}[/tex]

Step-by-step explanation:

Given the algebraic sentence

“Eleven more than eight times a number is -12“

Let us first breakdown the statement:

1st step:

Let the number be: x

2nd Step:

Eight times a number: 8x

Important Tip:

  • Note: When we say 'Eight times a number' it means we are just multiplying a number with 8 or we can say the product of 8 and a number.

3rd Step:

Eleven more than eight times a number: 8x + 11

Important Tip:

  • When we say 'Eleven more than eight times a number' it means we are just adding 11 into 8x.

Final Step:

Eleven more than eight times a number is -12: 8x + 11 = 12

Therefore, the algebraic sentence, “Eleven more than eight times a number is -12“, can be translated and written into an algebraic equation such as:

[tex]8x + 11 = 12[/tex]

We can further solve the equation such as

[tex]8x + 11 = 12[/tex]

Subtract 11 from both sides

[tex]8x+11-11=12-11[/tex]

Simplify

[tex]8x=1[/tex]

Divide both sides by 8

[tex]\frac{8x}{8}=\frac{1}{8}[/tex]

Simplify

[tex]x=\frac{1}{8}[/tex]

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