Solving Equations PDF

## 5.1 - Introduction to Solving Equations **Equation** - a statement showing that two mathematical expressions are equal. **Ex**. 2x + 3 = 11, 5x - 2 = 3x + 12, 2x² - 1 = 32 **Solve** - determine a value for the variable that makes an equation true. **Verify** - check if the solution value sati...

## 5.1 - Introduction to Solving Equations **Equation** - a statement showing that two mathematical expressions are equal. **Ex**. 2x + 3 = 11, 5x - 2 = 3x + 12, 2x² - 1 = 32 **Solve** - determine a value for the variable that makes an equation true. **Verify** - check if the solution value satisfies (i.e. balances) the equation. **Ex.1** Determine if x = 10 is a solution to each of the following equations. **(a)** 4x - 1 = 7 4(10) - 1 = 7 40 -1 = 7 39 ≠ 7 LS ≠ RS ∴ x = 10 is not a Solution **(b)** 5x - 8 = 4x + 2 5(10) - 8 = 4(10) + 2 50 - 8 = 40 + 2 42 = 42 LS = RS ∴ x = 10 is a Solution ## Inverse Operations | Addition | Subtraction and Multiplication | Division | |---|---|---| | 🠒 | 🠒 | 🠒 | **Ex. 2** Solve the following one-step equations. **(a)** x + 11 = 24 x + 11 - 11 = 24 - 11 **x = 13** **(b)** x - 5 = 7 x - 5 + 5 = 7 + 5 **x = 12** **(c)** 3x = 15 3x / 3 = 15 / 3 **x = 5** **(d)** x / 2 = 10 x / 2 * 2 = 10 * 2 **x = 20** ## Ex. 3 Solve the following two-step equations. **(a)** 3x + 1 = 7 3x + 1 -1 = 7 - 1 3x = 6 3x / 3 = 6 / 3 **x = 2** **(b)** -2x + 5 = 21 -2x + 5 - 5 = 21 - 5 -2x = 16 -2x / -2 = 16 / -2 **x = -8** **(c)** 6n -1 = 17 6n -1 + 1 = 17 + 1 6n = 18 6n / 6 = 18 / 6 **n = 3** **(d)** 14 - 3n = 38 14 - 3n - 14 = 38 - 14 -3n = 24 -3n / -3 = 24 / -3 **n = -8** ## Application **Ex. 4** The simplified perimeter formula for a rectangle is P = 4x - 3, where x is measured in cm. If the perimeter is 28 cm, determine x. P = 4x - 3 28 = 4x - 3 28 + 3 = 4x - 3 + 3 31 = 4x 31 / 4 = 4x / 4 **7.75 cm = x** **Ex. 5** Fido is offering a special on a cell phone plan. The monthly fee is $40 with a purchase of $250 for an iPhone. How many months of service can you get for $1210? Let n represent the unknown number of months. 1210 = 40n + 250 1210 - 250 = 40n + 250 - 250 960 = 40n 960 / 40 = 40n / 40 **24 = n** ∴ you can get 24 months of service.