How can an inequality be manipulated to show a specific range of values?

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In summary, an inequality is a mathematical statement that compares two quantities or expressions using symbols such as <, >, ≤, or ≥. Manipulating an inequality means to perform operations on both sides in order to solve for the variable. The rules for manipulating an inequality are the same as the rules for manipulating equations, with the exception of reversing the inequality symbol when multiplying or dividing by a negative number. To graph an inequality, first rewrite it in slope-intercept form if possible, plot the y-intercept, use the slope to find another point, and then shade the region above or below the line depending on the direction of the inequality symbol. It is important to consider the direction of the inequality symbol when solving and graphing inequalities in order to
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shawli
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In an example in my textbook, it says the following:

"If -1 ≤ x ≤ 1, then 0 ≤ x2 ≤ 1. "


Can someone explain to me how to move from the first statement to the second statement please? I'm not quite sure how the -1 turned into a 0...
 
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  • #2
Did you draw a graph of x^2 on the interval -1 ≤ x ≤ 1?
 
  • #3
Ah right... it's staring me right in the face! So clear that I missed it haha. Thank you!
 

FAQ: How can an inequality be manipulated to show a specific range of values?

What is an inequality?

An inequality is a mathematical statement that compares two quantities or expressions using symbols such as <, >, ≤, or ≥. It shows that one quantity is less than, greater than, less than or equal to, or greater than or equal to the other quantity.

What does it mean to manipulate an inequality?

Manipulating an inequality means to perform operations on both sides of the inequality in order to solve for the variable and find all possible solutions to the inequality.

What are the rules for manipulating an inequality?

The rules for manipulating an inequality are the same as the rules for manipulating equations. You can add, subtract, multiply, or divide both sides of the inequality by the same number or expression without changing the truth of the inequality. However, when multiplying or dividing by a negative number, the direction of the inequality symbol must be reversed.

How do you graph an inequality?

To graph an inequality, first rewrite it in slope-intercept form (y = mx + b) if possible. Then, plot the y-intercept (b) on the y-axis. Next, use the slope (m) to find another point on the line. If the inequality is < or >, the line will be dotted, and if it is ≤ or ≥, the line will be solid. Lastly, shade the region above or below the line depending on the direction of the inequality symbol.

Why is it important to consider the direction of the inequality symbol when solving and graphing inequalities?

The direction of the inequality symbol tells us which direction the solution set lies. If the inequality is < or >, the solution set will be a range of numbers. If the inequality is ≤ or ≥, the solution set will be a range of numbers including the endpoints. It is important to consider the direction when solving and graphing inequalities in order to accurately represent the solutions and to avoid making any errors in the process.

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