Question

Show ALL Work c), x+16% +63 = 0 D. Please Solve for x. For some problems, tell which results are the only solutions; or if there is no solution. a). .010.2x +.8)=.005% -1 b). {1x+5) = $ (3x +27) d) x ² 48²_9x+36=0 e). √x+21=8 f). Ý3x-9 =-6 g). √x+6 = x-6 h), biz * * -- I), X J. 1 3 3x - 1 + 1 = 2 / 4 K). 16 = 8 2x-1 2). 2 9 + 2 x+2 -6 2-/ x²+x-2 3% y3x+4 = 1

Answer 1

a)

0.01 (0.2х +0.8) = 0.005 — 0.1 0.002х + 0.008 = 0.005х — 0.1 0.003x = 0.108 =3x = 108 = х = 36

It is the only solution.

b)

$\bigskip \frac{4}{5}(x+5)=\frac{2}{3}(3x+27)\\\bigskip\Rightarrow \frac{4}{5}(x+5)=\frac{2}{3}\times 3(x+9) \\\bigskip\Rightarrow \frac{4}{5}(x+5)=2(x+9) \\\bigskip\Rightarrow2\times \frac{2}{5}(x+5)=2(x+9) \\\bigskip\Rightarrow \frac{2}{5}(x+5)=(x+9) \\\bigskip\Rightarrow 2(x+5)=5(x+9) \\\bigskip\Rightarrow 2x+10=5x+45 \\\bigskip\Rightarrow 3x=-35 \\\bigskip\Rightarrow x=-\frac{35}{3}$

It is the only solution

c)

$\bigskip x^2+16x+63=0\\\bigskip\Rightarrow x^2+2\times 8\times x+64=1 \\\bigskip\Rightarrow x^2+2\times 8\times x+8^2=1 \\\bigskip\Rightarrow (x+8)^2=1 \\\bigskip\Rightarrow x+8=\pm 1 \\\bigskip\Rightarrow x=-8\pm 1 \\\bigskip\Rightarrow x=-9 \text{ or }-7$

These are the only solutions for x

d)

$\bigskip x^3-4x^2-9x+36=0 \\\bigskip\Rightarrow (x-3)(x^2-x-12)=0 \\\bigskip\Rightarrow (x-3)(x^2-4x+3x-12)=0 \\\bigskip\Rightarrow (x-3)(x-4)(x+3)=0 \\\bigskip\Rightarrow x =-3,\enspace 3\text{ or }4$

These are the only solutions.