algebra with fractions While studying math, I have come across this problem: x<x/3+2/3 Now according to the textbook, the answer is x<1, but I can't see how they came up with that solution, as I could only come up with the answer x<x+2. So I'd appreciate it if someone could explain this to me.

Agostarawz

Agostarawz

Answered question

2022-07-13

algebra with fractions
While studying math, I have come across this problem:
x < x 3 + 2 3
Now according to the textbook, the answer is x < 1, but I can't see how they came up with that solution, as I could only come up with the answer x < x + 2. So I'd appreciate it if someone could explain this to me.

Answer & Explanation

Sariah Glover

Sariah Glover

Beginner2022-07-14Added 16 answers

Subtracting x 3 from both sides
2 x 3 < 2 3
Multiplying both sides by 3 2 gives
x < 1
Esmeralda Lane

Esmeralda Lane

Beginner2022-07-15Added 7 answers

x < x 3 + 2 3 3 3 x < x + 2 x 2 x < 2 ÷ 2 x < 1
Observe that all the involved operations, carried on both sides of the inequality, do not change the inequality sign...

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