Lesson 3.4

f(x) = g(x) ↔ f(x) + h(x) = g(x) + h(x)

If h ≠ 0, then,f(x) = g(x) ↔ f(x) • h(x) = g(x) • h(x)

Solve . Identify the property used to justify each step.

Conclusion: Justification: x4-18 = 3(2x2+3) - mult. Prop. Of

equ.x4-18 = 6x2+9 - distributive prop.x4- 6x2 -27 =0 - addition prop.(x2-9)(x2+3) = 0 - distributive propx = 3, x = -3 - zero product.Check; both work!

-2(x2-8x+15) = 2x – 6 -mult. Prop. -2x2+16x-30 = 2x – 6 - dist. Prop. -2x2+14x -24 = 0 -add. Prop -2(x2-7x+12) = 0 -dist. Prop -2(x-3)(x-4) = 0 -dist. Prop x = 3, x = 4 -zero

product. 3 doesn’t work!! x = 4

Reversible they are bi-conditional (can be undone)

Irreversible true conditional (if-then) statements for which the converse is false• Squaring both sides• Taking the log of both sides• Taking the square root of both sides• Multiplying out the denominator

If a function is 1-1, then the step is reversible. (x3, )

Find all real numbers x satisfying 32x-5 = 2187

Log32187 =2x-5 change to logLog2187/log3 =2x-5 change of base

7 = 2x – 5 12 = 2x addition

x = 6 mult.

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