2 4 Equations and Their Solutions Learn to

2 -4 Equations and Their Solutions Vocabulary equation solution

2 -4 Equations and Their Solutions An equation is a mathematical statement that two

2 -4 Equations and Their Solutions Equations may contain variables. If a value for

2 -4 Equations and Their Solutions Reading Math The symbol means “is not equal

2 -4 Equations and Their Solutions Additional Example 1 A: Determining Solutions of Equations

2 -4 Equations and Their Solutions Additional Example 1 B: Determining Solutions of Equations

Equations and Their Solutions 2 -4 Check It Out: Example 1 A Determine whether

Equations and Their Solutions 2 -4 Check It Out: Example 1 B Determine whether

2 -4 Equations and Their Solutions Reading Math An equation has an equal sign,

2 -4 Equations and Their Solutions Additional Example 2 Paulo says that his yard

2 -4 Equations and Their Solutions Check It Out: Example 2 Anna says that

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2 -4 Equations and Their Solutions Learn to determine whether a number is a solution of an equation.

2 -4 Equations and Their Solutions Vocabulary equation solution

2 -4 Equations and Their Solutions An equation is a mathematical statement that two expressions are equal. You can think of a correct equation as a balanced scale. 3+2 5

2 -4 Equations and Their Solutions Equations may contain variables. If a value for a variable makes an equation true, that value is a solution of the equation. s + 15 = 27 s = 12 12 + 15 s = 10 27 s = 12 is a solution because 12 + 15 = 27. 10 + 15 27 s = 10 is not a solution because 10 + 15 27.

2 -4 Equations and Their Solutions Reading Math The symbol means “is not equal to. ”

2 -4 Equations and Their Solutions Additional Example 1 A: Determining Solutions of Equations Determine whether the given value of the variable is a solution. b — 447 = 1, 203 for b = 1, 650 b — 447 = 1, 203 ? 1, 650 — 447 = 1, 203 ? 1, 203 = 1, 203 Substitute 1, 650 for b. Subtract. Because 1, 203 = 1, 203, 1, 650 is a solution to b — 447 = 1, 203.

2 -4 Equations and Their Solutions Additional Example 1 B: Determining Solutions of Equations Determine whether the given value of the variable is a solution. 27 x = 1, 485 for x = 54 27 x = 1, 485 ? 27 54 = 1, 485 ? 1, 458 = 1, 485 1, 458 1, 485 Substitute 54 for x. Multiply. Because 1, 458 1, 485, 54 is not a solution to 27 x = 1, 485.

Equations and Their Solutions 2 -4 Check It Out: Example 1 A Determine whether the given value of the variable is a solution. u + 56 = 139 for u = 73 u + 56 = 139 ? 73 + 56 = 139 ? 129 = 139 129 139 Substitute 73 for u. Add. Because 129 139, 73 is not a solution to u + 56 = 139.

Equations and Their Solutions 2 -4 Check It Out: Example 1 B Determine whether the given value of the variable is a solution. 45 g = 3 for g = 15 45 g = 3 ? 45 15 = 3 Substitute 15 for g. ? Divide. 3=3 3 3 Because 3 = 3, 15 is a solution to 45 g = 3.

2 -4 Equations and Their Solutions Reading Math An equation has an equal sign, but an expression does not. An equation can be solved, but an expression can only be evaluated or simplified.

2 -4 Equations and Their Solutions Additional Example 2 Paulo says that his yard is 19 yards long. Jamie says that Paulo’s yard is 664 inches long. Determine if these two measurements are equal. 36 yd = in. ? 36 19 = 664 ? 684 = 664 Substitute. Multiply. Because 684 664, 19 yards is not equal to 664 inches.

2 -4 Equations and Their Solutions Check It Out: Example 2 Anna says that the table is 7 feet long. John says that the table is 84 inches long. Determine if these two measurements are equal. 12 ft = in. ? 12 7 = 84 ? 84 = 84 Substitute. Multiply. Because 84 = 84, 7 feet is equal to 84 inches.