Question

1. Rezolvati , in multimea numerelor naturale , ecuatiilt .
a)2 (x+3) + 17 = 59
b)5 (x-1)+11=26
c)3 (x+5)+6=33
d)8 (x-1) + 15 = 55
e)10 (x+2) + 17 = 67
f)9 (x-3)-23 =22
g)2 (2x-3)-9=1
h)2+3(x+1) =10
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Answer 1

$\displaystyle a)2 (x+3) + 17 = 59 \Rightarrow 2x+6+17=59 \Rightarrow 2x=59-6-17 \Rightarrow \\ \\ \Rightarrow 2x=36 \Rightarrow x= \frac{36}{2} \Rightarrow \boxed{x=18} \\ \\ b)5 (x-1)+11=26 \Rightarrow 5x-5+11=26 \Rightarrow 5x=26+5-11 \Rightarrow \\ \\ \Rightarrow 5x=20 \Rightarrow x= \frac{20}{5} \Rightarrow \boxed{x=4} \\ \\ c)3 (x+5)+6=33 \Rightarrow 3x+15+6=33 \Rightarrow 3x=33-15-6 \Rightarrow \\ \\ \Rightarrow 3x=12 \Rightarrow x= \frac{12}{3} \Rightarrow \boxed{x=4}$

$\displaystyle d)8 (x-1) + 15 = 55 \Rightarrow 8x-8+15=55 \Rightarrow 8x=55+8-15 \Rightarrow \\ \\ \Rightarrow 8x=48 \Rightarrow x= \frac{48}{8} \Rightarrow \boxed{x=6} \\ \\ e)10 (x+2) + 17 = 67 \Rightarrow 10x+20+17=67 \Rightarrow 10x=67-20-17 \Rightarrow \\ \\ \Rightarrow 10x=30 \Rightarrow x= \frac{30}{10} \Rightarrow \boxed{x=3} \\ \\ f)9 (x-3)-23 =22 \Rightarrow 9x-27-23=22 \Rightarrow 9x=22+27+23 \Rightarrow \\ \\ \Rightarrow 9x=72 \Rightarrow x= \frac{72}{9} \Rightarrow \boxed{x=8}$

$\displaystyle g)2 (2x-3)-9=1 \Rightarrow 4x-6-9=1 \Rightarrow 4x=1+6+9 \Rightarrow \\ \\ \Rightarrow 4x=16 \Rightarrow x= \frac{16}{4} \Rightarrow \boxed{x=4}\\ \\ h)2+3(x+1) =10 \Rightarrow 2+3x+3=10 \Rightarrow 3x=10-2-3 \Rightarrow \\ \\ \Rightarrow 3x=5 \Rightarrow \boxed{x= \frac{5}{3} }$