Answer :
Final answer:
The values of x that satisfy the inequalities x-16 <=20 and x+12 >7 are all numbers greater than -5 and less than or equal to 36.
Explanation:
The student is asked to solve for x in the following inequalities: x-16 <=20 and x+12 >7. These inequalities can be solved by simple manipulations to separate x. The first can be solved by adding 16 to both sides of the inequality, resulting in x <= 36. The second is solved by subtracting 12 from both sides, resulting in x > -5. The values of x that satisfy both conditions are all the numbers greater than -5 up to 36.
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Final answer:
The values of x that satisfy the inequalities x-16≤20 and x+12>7 are x ≤ 36 and x > -5.
Explanation:
To solve the first inequality, x-16≤20, we can add 16 to both sides to isolate x: x ≤ 20 + 16, which simplifies to x ≤ 36.
For the second inequality, x+12>7, we can subtract 12 from both sides to isolate x: x > 7 - 12, which simplifies to x > -5.
So, combining both inequalities, we have x ≤ 36 and x > -5. These are the values of x that satisfy both inequalities.
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