Answer:
[tex]a) x=\frac{4}{45}[\\\\b) x=-\frac{19}{5}\\\\c)x=20\\\\d)x=5\\\\e)x=\frac{11}{7}\\\\f) x=17[/tex]
Step-by-step explanation:
a) Given the proportion:
[tex]\frac{2}{15}=\frac{3}{2}x[/tex]
You must solve for "x":
[tex](\frac{2}{3})(\frac{2}{15})=x\\\\x=\frac{4}{45}[/tex]
b) Given:
[tex]\frac{9}{4}=\frac{x+2}{x+3}[/tex]
Solve for "x":
[tex](x+3)(\frac{9}{4})=x+2\\\\\frac{9}{4}x+\frac{27}{4}=x+2\\\\\frac{9}{4}x-x=2-\frac{27}{4}\\\\\frac{5}{4}x=-\frac{19}{4}\\\\x=(-\frac{19}{4})(\frac{4}{5})\\\\x=-\frac{19}{5}[/tex]
c) [tex]\frac{x+5}{x}=\frac{10}{8}[/tex]
Solve for "x":
[tex]x+5=\frac{10}{8}x\\\\5=\frac{10}{8}x-x\\\\5=\frac{1}{4}x\\\\(5)(4)=x\\\\x=20[/tex]
d) [tex]\frac{3x}{21}=\frac{5}{7}[/tex]
Solve for "x":
[tex]3x=(\frac{5}{7})(21)\\\\x=\frac{15}{3}\\\\x=5[/tex]
e) [tex]\frac{2x-1}{x+2}=\frac{3}{5}[/tex]
Solve for "x":
[tex](5)(2x-1)=(3)(x+2)\\\\10x-5=6x+6\\\\10x-3x=6+5\\\\7x=11\\\\x=\frac{11}{7}[/tex]
f) [tex]\frac{x-5}{3}=\frac{x-1}{4}[/tex]
Solve for "x":
[tex](4)(x-5)=(x-1)(3)\\\\4x-20=3x-3\\\\4x-3x=-3+20\\\\x=17[/tex]
