Fundamentals of Math - old

Fundamentals of Mathematics

3.4 Simplifying and Solving Linear Equations In order to solve the equations, it is important to move all variables to one side using inverse operations (addition ⟷ subtraction & multiplication ⟷ division). It should be noted that applying inverse operations on both sides of an equation keeps the balance. For instance, the equation – 3 = 7 can be simplified by adding 3 on each side, − 3 + 3 = 7 + 3 . Thus; the final answer is = 10 . More examples are shown on the next page.

Example 3.4.1, 3.4.2, and 3.4.3

Equation

Steps

(2 + 10) 2

Step 1: Multiply both sides by 2 2 + 10 2 × 2 = 35 × 2

= 35

2 + 10 = 70

2 = 60

Step 2: Subtract 10 from both sides

2 + 10 − 10 = 70 − 10

=

Step 3: Divide both sides by 2 2 2 = 60 2

Step 1: Simplify the equation

– 6– 5 = 3

2

– 11 = 3

2

Step 2: Add 11 to both sides

= 14

2

2 – 11 + 11 = 3 + 11

=

Step 3: Multiply both sides by 2

× 2 = 14 × 2

2

Step 1: Simplify the equation 2 × 2 2 × 1 − 2 + 13 = 28

2 –

2 + 10 − 12 + 15 = 28 3 2 + 13 = 28

3

Step 2: Subtract 13 from both sides 3 2 + 13– 13 = 28– 13 Step 3: Multiply both sides by 2 3 3 2 × 2 3 = 15 × 2 3

= 15

2

=

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