How do you write an inequality and solve given "three fourths of a number decreased...

Villaretq0

Villaretq0

Answered

2022-06-28

How do you write an inequality and solve given "three fourths of a number decreased by nine is at least forty two"?

Answer & Explanation

tennispopj8

tennispopj8

Expert

2022-06-29Added 20 answers

Step 1
First, let's call "a number" n
"three fourths of a number" then can be written as:
3 4 n
This, "decreased by nine" then can be written as:
3 4 n - 9
"is at least" is the same as so we can now write:
3 4 n - 9
and what it is "at least" is "forty two" so:
3 4 n - 9 42
To solve this we first add 9 to each side of the inequality to isolate the n term while keeping the inequality balanced:
3 4 n - 9 + 9 42 + 9
3 4 n - 0 51
3 4 n 51
Now, we multiply each side of the inequality by 4 3 tosolve for n while keeping the inequality balanced:
4 3 × 3 4 n 4 3 × 51
4 3 × 3 4 n 4 × 17
n 68
Taniyah Estrada

Taniyah Estrada

Expert

2022-06-30Added 5 answers

Step 1
Let's use some punctuation so show exactly what is meant: note how the placement of a comma gives a different meaning.
three fourths of a number , decreased by 9 is at least 42
Let the number be x
3 4 x - 9 42
Solving gives:
3 4 x 51
4 3 × 3 4 x 51 × 4 3
x 56
However, if we interpret it differently we could have:
three fourths of, a number decreased by 9, is at least 42
3 4 ( x - 9 ) 42
Solving gives:
4 3 × 3 4 ( x - 9 ) 42 × 4 3
x - 9 56
x 65

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