Equations and Solutions Core Focus on Introductory Algebra Lesson 3.1.

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Equations and Solutions Core Focus on Introductory Algebra Lesson 3.1

Evaluate each expression. 1.y − 14 when y = x when x = 0 3.(a − 3) 2 when a = 10 Warm-Up

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

Equation A mathematical sentence that contains an equals sign (=) between two expressions. Solution A value that makes an equation true. Vocabulary x + 7 = = = 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.

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.

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) = = 32A SOLUTION.

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.

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

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

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 = 5Is 1.82 the solution? Exit Problems No Yes