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Examples and rules for solving linear equations with one unknown variable, applying the rule of power, and solving equations with two unknown variables. Students enrolled in economics 303 or similar courses will find this review helpful for understanding mathematical concepts essential for their studies.
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Example 1: 3x = 5 x = 5/3 = 1. 67 Example 2: 1.5 + 3x = 6 + 1. 5 x
3 x − 1. 5 x = 6 − 1. 5
3 x + 2x = 1 5 x = 1 x = 1/5 = 0. 2 Example 4: 12(x − 5) = 3(x + 10) 12 x − 60 = 3x + 30 12 x − 3 x = 30 + 60 9 x = 90 x = 90/9 = 10 Example 5: (^5) x = 6
5 = 6x x = 5/ 6
Let a and b any real number. xa^ · xb^ = xa+b xa xb^ =^ x
a−b x−a^ = (^) x^1 a (xa)b^ = xa·b (xa)^1 /a^ = xa·^1 /a^ = x Example 1: x^0.^5 = 7
x = 7^1 /^0.^5 = 49 Example 2: 7x^0.^3 = 5x (^7)
5 =^
x x^0.^3 1 .4 = x^1 −^0.^3 x^0.^7 = 1. 4 x = 1. 41 /^0.^7 Example 3: (^) x^50. 3 = 2x^2 5 2 =^ x (^2) · x 0. 3 x^2.^3 = 2. 5 x = 2. 51 /^2.^3 Example 4: √ 3 − 5 x = 2 3 − 5 x = 2^2 = 4 5 x = 3 − 4 = − 1 x = − 1 / 5 Example 5: √x = 2√ 5 − x
x = 4(5 − x) x = 20 − 4 x x + 4x = 5x = 20 x = 20/5 = 4
