There is some overlap among these topics, so I recommend reading the whole page. Ultimately, what are the sources of errors and of misunderstanding? What kinds of biases and erroneous preconceptions do we have?

What happens if we multiply both numbers by the same value c? The exercise below will let us find out. On this number line, points B and A are our original values of 2 and 5. The inequality has been maintained.

This is written formally as: If we take the same two numbers and multiply them by The resulting value of AC This pattern holds true for all inequalities—if they are multiplied by a negative number, the inequality flips.

The Division Properties of Inequality work the same way.

If we divide both sides by a positive number, the inequality is preserved. To put it mathematically: If we divide both side of an inequality by a negative number, the inequality is reversed.

What relationship would she expect to see between the two stocks at the end of Tuesday? The stocks were not worth the same amount in the beginning, so if each stock loses half its value, the new values will not be equal either. For example, here is a problem where we can use the Subtraction Property to help us find a range of possible solutions: In 7 years, Ellie will be old enough to vote in an election.

You must be at least 18 years old to vote. What can you say about how old she is now? We could write this inequality as: We can then use the Subtraction Property of Inequality to solve for e.Writing, Solving, and Graphing Inequalities in One Variable.

Learning Objective · Solve algebraic inequalities in one variable using a combination of the properties of inequality. · . Write Inequalities with Write an inequality for each sentence. You must be over 12 years old to ride the go-karts. Words Variable Inequality Your age is over Let a = your age.

a > 12 The inequality is a > A pony is less than hands tall. Words Variable Inequality A pony is less than Let p = the height of the pony p. Apr 22, · Best Answer: PROBLEM 1: Just look at the line first. It has a slope of You can use the two intercept points to figure the slope, or you can figure out the rise (-1) over the run (1).

The y-intercept is 4 because the line goes through the y-axis at (0,4) The slope-intercept form of a line is: y = mx + b Status: Resolved. Write Inequalities with Write an inequality for each sentence. You must be over 12 years old to ride the go-karts. Words Variable Inequality Your age is over Let a = your age.

a > 12 The inequality is a > A pony is less than hands tall. Words Variable Inequality A pony is less than Let p = the height of the pony p. This page describes the errors that I have seen most frequently in undergraduate mathematics, the likely causes of those errors, and their remedies.

To find the inequality, we need to remember our rules about what makes inequalities from number lines. If the "dot" (initial point) is hollow, it is simply a "" symbol. If the "dot" is filled in, it means that it includes that number and we should use a "≤" or "≥" symbol/5(2).

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Graphing Linear Inequalities