Question
Solve 32 < 2x < 46.
- 12 < x < 23
- x > 23
- 16 < x
- 16 < x < 23
Hint:
We are given an expression of compound inequality. A compound inequality means we are given two statements i.e. inequalities. We have to find the values of the variables satisfying those statements. We will simply the expressions using the rules to solve the inequalities.
The correct answer is: 16 < x < 23
The given statement is 32 < 2x < 46.
The quantity 2x is less than 46 and is greater than 32.
We will solve the problem using the rules to solve the inequalities.
We have to perform the same operation on all three terms.
32 < 2x < 46
We will divide all the three terms by 2. The sign of inequality is not flipped as we are dividing by positive numbers.
16 < x < 23
We cannot simplify it further.
So, the final answer is 16 < x < 23.
We have to follow the rules of inequalities to solve such questions. We have to swap the inequality when we divide it or multiply it by a negative number. In such questions, we find the values of the variables which makes the statement of inequalities true.
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