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Definitions of Equations, Inequalities, and Slopes

Define the term equation and then explain what it means to solve an equation. Give an example of an equation and its solution. Explain why it is the solution.

Define the term linear inequality and then explain what it means to solve a linear inequality. Explain how the solution to the inequality 2x-5<25 differs from the solution to the equation 2x-5=25.

Explain the concept of slope. How does the slope of a line represent a rate of change? Given the equation d = 3t-2, explain how the variable d is changing with respect to the variable t.

Solution Preview

An equation is a condition where two algebraic expressions are the same. Solving it means that you find all values that you can substitute in place of the variable so that the resulting numbers are equal. The equation 2x + 4 = 10 has a solution of x = 3 because 2*3 + 4 is the same as the number 10 when simplified. x = 5 is not a solution because 2*5 + 4 is equal to 14, not 10. Solving the equation is the process that involves finding out what you can put in place of x that makes both sides of the ...

Solution Summary

Define the term equation and then explain what it means to solve an equation. Give an example of an equation and its solution. Explain why it is the solution.

Define the term linear inequality and then explain what it means to solve a linear inequality. Explain how the solution to the inequality 2x-5<25 differs from the solution to the equation 2x-5=25.

Explain the concept of slope. How does the slope of a line represent a rate of change? Given the equation d = 3t-2, explain how the variable d is changing with respect to the variable t.

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