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Hannah is 2 times her sister’s age. The sum of their ages is no more than 18 years. 1) Write an inequality that can be used to represent this situation. 2) Using the inequality you just found, solve it to find the oldest age Hannah's sister can be.

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Answer:

1) [tex]x+2x\leq 18[/tex].

2) [tex]6[/tex] years

Step-by-step explanation:

Let Hanna's sister be [tex]x[/tex] years old.


Then Hanna will be [tex]2x[/tex] years old.


The sum of their ages will be [tex]x+2x[/tex] years.

The statement "no more than 18" means the sum of their ages is less than or equal to 18.

The required inequality is;

[tex]x+2x\leq 18[/tex].

2)

The inequality we just found is


[tex]x+2x\leq18[/tex].

We simplify to get;

[tex]3x\leq 18[/tex].

we divide both sides by [tex]3[/tex] to get;

[tex]x\leq 6[/tex].

Therefore the oldest age Hannah's sister can be is [tex]6[/tex] years




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