1. Equations and Solutions Core Focus on Introductory Algebra Lesson 3.1

2. Evaluate each expression. 1.y − 14 when y = 29 2.7 + 2x when x = 0 3.(a − 3) 2 when a = 10 Warm-Up 15 7 49

3. Equations and Solutions Determine if a number is a solution of an equation. Lesson 3.1

4. Equation A mathematical sentence that contains an equals sign (=) between two expressions. Solution A value that makes an equation true. Vocabulary x + 7 = 20 13 + 7 = 20 20 = 20 The equation. The equation is true. The value of x that makes this equation true is 13. Thirteen is the solution of the equation.

5. Determine if the number given is the solution of the equation. a.x − 5 = 12 Is 7 the solution? Substitute the given value for the variable into the equation to see if it makes the equation true. Example 1 x − 5 = 12 7 − 5 = 12 2  12NOT A SOLUTION. The  symbol shows that one side of the expression is “not equal to” the other side of the expression.

6. Determine if the number given is the solution of the equation. b.8y = 32Is 4 the solution? Substitute 4 for y to see if it makes the equation true. Example 1 Continued… 8y = 32 8(4) = 32 32 = 32A SOLUTION.

7. Determine if the number given is the solution of the equation. c.Is 27 the solution? Substitute 27 for m to see if it makes the equation true. Example 1 Continued… A SOLUTION.

8. Identify whether each number in the table is a solution of the equation. Each value must be substituted for the variable to determine if it is a solution. Remember that the number is only a solution if it makes the equation true. x14 − x = 8Solution? 414 − (4) ≠ 8No 614 − (6) = 8Yes 914 − (9) ≠ 8No Example 2

9. How can you tell if a number is a solution of an equation? Illustrate the process with your own example. Communication Prompt

10. Determine if the number given is the solution of the equation. 1.b + 15 = 24Is 11 the solution? 2.9a = 54Is 7 the solution? 3.32 − x = 19Is 13 the solution? 4.w + 3.18 = 5Is 1.82 the solution? Exit Problems No Yes