Question

a/ 5^x+3 +5^x=126

\(\dfrac{9-3x}{2}=\dfrac{5-2x}{3}\)

c/ 7-4(x+1)=5

 

Answer 1

a) \(5^{x+3}+5^x=126\)

\(\Rightarrow5^x\cdot\left(5^3+1\right)=126\)

\(\Rightarrow5^x\cdot\left(125+1\right)=126\)

\(\Rightarrow5^x=\dfrac{126}{126}\)

\(\Rightarrow5^x=1\)

\(\Rightarrow5^x=5^0\)

\(\Rightarrow x=0\)

b) \(\dfrac{9-3x}{2}=\dfrac{5-2x}{3}\)

\(\Rightarrow\dfrac{3\cdot\left(9-3x\right)}{6}=\dfrac{2\cdot\left(5-2x\right)}{6}\)

\(\Rightarrow3\cdot\left(9-3x\right)=2\cdot\left(5-2x\right)\)

\(\Rightarrow27-9x=10-4x\)

\(\Rightarrow-4x+9x=27-10\)

\(\Rightarrow5x=17\)

\(\Rightarrow x=\dfrac{17}{5}\)

c) \(7-4\left(x+1\right)=5\)

\(\Rightarrow4\left(x+1\right)=7-5\)

\(\Rightarrow4\left(x+1\right)=2\)

\(\Rightarrow x+1=\dfrac{1}{2}\)

\(\Rightarrow x=\dfrac{1}{2}-1\)

\(\Rightarrow x=-\dfrac{1}{2}\)