# Equations and Their Solutions

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Equations and Their Solutions
2-4 Equations and Their Solutions Warm Up Problem of the Day Lesson Presentation Course 1 Course 1

Warm Up Evaluate each expression for x = 8. 1. 3x + 5 2. x + 8
29 16 9 16 55 5

Problem of the Day Complete the magic square so that every row, column, and diagonal add up to the same total. 10 7 4 9 2 8 6 12 5

Learn to determine whether a number is a solution of an equation.

Vocabulary equation solution

An equation is a mathematical statement that two quantities are equal
An equation is a mathematical statement that two quantities are equal. You can think of a correct equation as a balanced scale. 3 + 2 5

s = 12 is a solution because 12 + 15 = 27.
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 s = 10 27 27 s = 12 is a solution because = 27. s = 10 is not a solution because  27.

Additional Example 1A: 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 ? Substitute 1,650 for b. 1,203 = 1,203 ? Subtract. 1,203 Because 1,203 = 1,203, 1,650 is a solution to b — 447 = 1,203.

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

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

Determine whether the given value of the variable is a solution.
Check It Out: Example 1B 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. 3 = 3 ? Divide. 3 Because 3 = 3, 15 is a solution to 45  g = 3.

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 ? Substitute. 684 = 664 ? Multiply. Because 684  664, 19 yards are not equal to 664 inches.

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 ? Substitute. 84 = 84 ? Multiply. Because 84 = 84, 7 feet is equal to 84 inches.

Lesson Quiz Determine whether the given value of each variable is a solution. 1. 85 = 13x for x = 5 2. w + 38 = 210 for w = 172 3. 8y = 88 for y = 11 4. 16 = w  6 for w = 98 no yes yes no 5. The local pizza shop charged Kylee \$172 for 21 medium pizzas. The price of a medium pizza is \$8. Determine if Kylee paid the correct amount of money. (Hint: \$8 • pizzas = total cost.) no