LINEAR INEQUALITIES
We solve linear inequalities using the same properties, with one additional consideration.
When multiplying or dividing both sides of an inequality by a blank number, reverse the inequality sign. Notice that the solution is a set of numbers.
Inequalities have an infinite blank.
Answer (2)
When solving linear inequalities, if you multiply or divide both sides by a negative number, the inequality sign must be reversed. Inequalities have an infinite number of solutions, meaning there are countless numbers that can satisfy them. These properties are crucial for accurately understanding and solving inequalities in mathematics.
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When multiplying or dividing an inequality by a negative number, the inequality sign reverses.
Inequalities typically have an infinite number of solutions.
The completed statements are:
When multiplying or dividing both sides of an inequality by a negative number, reverse the inequality sign.
Inequalities have an infinite number of solutions.
The final answer is: negative, number n e g a t i v e , n u mb er .
Explanation
Analyzing the Statements Let's analyze the given statements about linear inequalities. The first statement discusses a crucial rule when manipulating inequalities, and the second highlights a fundamental property of their solutions.
Filling the First Blank The first statement says: 'When multiplying or dividing both sides of an inequality by a number, reverse the inequality sign.' We know that this happens when the number is negative. For example, if we have the inequality x < 2 , and we multiply both sides by -1, we get -2"> − x > − 2 . The inequality sign flips.
Filling the Second Blank The second statement says: 'Inequalities have an infinite .' This refers to the number of solutions. For example, the inequality 1"> x > 1 has infinitely many solutions, since any number greater than 1 satisfies the inequality.
Final Answer Therefore, the completed statements are:
LINEAR INEQUALITIES We solve linear inequalities using the same properties, with one additional consideration. When multiplying or dividing both sides of an inequality by a negative number, reverse the inequality sign. Notice that the solution is a set of numbers.
Inequalities have an infinite number of solutions.
Examples
Linear inequalities are used in various real-world scenarios. For example, when budgeting, you might have an inequality that represents the amount of money you can spend. If you have $100 and want to buy items that cost $10 each, the inequality would be 10 x ≤ 100 , where x is the number of items. Solving this inequality helps you determine the maximum number of items you can buy. Another example is in setting speed limits on roads; the speed limit is the maximum safe speed, represented by an inequality.
