This document discusses solving equations. It explains that solving an equation means finding the values of variables that make the equation true. Inverse operations are used to solve equations by undoing operations. The document provides examples of solving equations, writing equations from word problems, and determining whether equations are always, sometimes, or never true. It also covers solving literal equations by finding a variable in terms of other variables.

1. 1.4 Solving Equations

2. Solving Equations An equation is a statement in which two expressions are equal. Solving an equation that contains a variable means finding all values of the variable that make the equation true. A solution of the equation is a value that makes the equation true. Inverse operations are operations that “undo” each other. Inverse operations are used to solve equations

3. Solve each equation

4. Solve each equation

5. Solve each equation

6. Solve each equation

7. Write an equation to solve each problem. The flower carpet at Grand Place in Brussels, Belgium has a length that is three times the width and a perimeter of 200 meters. What are the dimensions?

8. Write an equation to solve each problem. Two buses leave Dallas at the same time and travel in opposite directions. One bus averages 58mi/h and the other averages 52mi/h. When will they be 363 mi apart?

9. Solutions An equation does not always have one solution. An equation has no solution if no value of the variable makes the equation true. When solving you will reach a false statement An identity is an equation that is true for every value of the variable. When solving you will reach a point where one side is identical to the other

10. Is the equation always, sometimes, or never true?

11. Is the equation always, sometimes, or never true?

12. Is the equation always, sometimes, or never true?

13. You Try It: Is the equation always, sometimes, or never true?

14. You Try It: Is the equation always, sometimes, or never true?

15. Literal Equations A literal equation is an equation that uses at least two different letters as variables. We usually solve literal equations “in terms of” one of the variables.

16. Solve for r

17. Solve for x

18. Solve for v