[tex]21) \\ \\ a) \frac{x + 1}{2} - \frac{x - 1}{5} = 6 \\ \\ 5(x + 1) - 2(x - 1) = 60 \\ \\ 5x + 5 - 2x + 2 = 60 \\ \\ 3x + 7 = 60 \\ \\ 3x = 60 - 7 = 53 \\ \\ x = \frac{53}{3} [/tex]
[tex]b) \frac{2x + 1}{3} + 3x = \frac{5}{2} \\ \\ 2x + 1 + 9x = \frac{15}{2} \\ \\ 11x + 1 = \frac{15}{2} \\ \\ 11x = \frac{15}{2} - 1 \times \frac{2}{2} = \frac{15}{2} - \frac{2}{2} = \frac{15 - 2}{2} \\ \\ 11x = \frac{13}{2} \\ \\ x = \frac{ \frac{13}{2} }{11} = \frac{13}{2 \times 11} = \frac{13}{22} [/tex]
[tex]c) \frac{x - 1}{2} + 3(x + 1) = \frac{5x}{3} \\ \\ 3(x - 1) + 18(x + 1) = 10x \\ \\ 3x - 3 + 18x + 18 = 10x \\ \\ 21x + 15 = 10x \\ \\ 15 = 10x - 21 \\ \\ 15 = - 11x \\ \\ - \frac{15}{11} = x \\ \\ x = - \frac{15}{11} [/tex]
22)
a)3x-2≤13
3x≤13+2
3x≤15
x≤[tex] \frac{15}{3} [/tex]
x≤5
b)2-3x<3-x
-3x-3-x-2
-3x<1-x
-3x+x<1
-2x<1
[tex]x > - \frac{1}{2} [/tex]
c)4(x-1)+3≥11
4(x-1)≥11-3
4(x-1)≥8
x-1≥[tex] \frac{8}{4} [/tex]
x-1≥2
x≥2+1
x≥3
d)5-3(x+1)>2x-6
5-3x-3>2x-6
-3x+2>2x-6
2>2x-6+3x
2>5x-6
2+6>5x
8>5x
[tex] \frac{8}{5} > x \\ \\ x < \frac{8}{5} [/tex]
20)
a)2x+3(x-3)=1
2x+3x-9=1
5x-9=1
5x=1+9=10
[tex]x = \frac{10}{5} = 2[/tex]
b)3(x+1)-2(x+3)=5
3x+3-2x-6=5
x-3=5
x=5+3=8
c)5x-7=2(x+3)
5x-7=2x+6
5x=2x+6+7
5x=2x+13
5x-2x=13
3x=13
[tex]x = \frac{13}{3} [/tex]
