Solving Inequalities: Need Help with Part (a)?

Thread starter mopit_011
Start date Mar 27, 2022
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Inequalities

In summary, an inequality is a mathematical statement that compares two quantities or expressions using symbols such as <, >, ≤, ≥. To solve an inequality, the variable must be isolated on one side of the symbol by performing operations on both sides, with the exception of flipping the symbol when multiplying or dividing by a negative number. The main difference between solving an equation and an inequality is the solution set, as an inequality has a range of possible solutions rather than a single value. Common mistakes when solving inequalities include forgetting to flip the symbol and making errors in distribution and order of operations. Inequalities have many real-life applications, such as representing relationships between quantities and solving problems in various fields.

Mar 27, 2022

mopit_011

Homework Statement: An object, constrained to move along the x axis, travels a dis-
tance d1 with constant velocity v1 for a time t1 . It then instan-
taneously changes its velocity to a constant v2 for a time t2 ,
traveling a distance d2 . (a) Show that (v1d1+v2d2)/(d1+d2) is greater than or equal to (v1t1+v2t2)/(t1+t2).
(b) Under what conditions is this an equality?

Relevant Equations: v = v0 + at
x = x0 + v0t + (at^2/2)

I’m not sure of how begin solving for the inequality. How do I begin solving part (a)? Could I have a hint? Thank you!

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Mar 27, 2022

haruspex

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A good start would be to write the expression for the difference between them.

What are inequalities?

Inequalities are mathematical expressions that compare two quantities or values. They use symbols such as <, >, ≤, and ≥ to show the relationship between the two quantities.

How do you solve inequalities?

To solve inequalities, you need to follow the same basic rules as solving equations. However, if you multiply or divide by a negative number, you must flip the inequality sign. Also, if you add or subtract a negative number, you must change the direction of the inequality sign.

What is the difference between solving equations and solving inequalities?

The main difference between solving equations and solving inequalities is that when solving inequalities, you must consider the direction of the inequality sign and make appropriate adjustments when multiplying, dividing, adding, or subtracting.

What is the purpose of solving inequalities?

The purpose of solving inequalities is to find the range of values that satisfy the given inequality. This is useful in many real-world applications, such as budgeting, determining acceptable values in scientific experiments, and analyzing data.

What are some common mistakes when solving inequalities?

Some common mistakes when solving inequalities include forgetting to flip the inequality sign when multiplying or dividing by a negative number, not considering the direction of the inequality sign when adding or subtracting, and not simplifying the expression before solving. It is important to double-check your work and make sure all steps are correct to avoid these mistakes.