Answer:
[tex]b=\dfrac{8}{3}[/tex]
Step-by-step explanation:
Given equation:
[tex]\dfrac{1}{b}+10=\dfrac{9}{b}+7[/tex]
Subtract 10 from both sides:
[tex]\implies \dfrac{1}{b}+10-10=\dfrac{9}{b}+7-10[/tex]
[tex]\implies \dfrac{1}{b}=\dfrac{9}{b}-3[/tex]
Multiply both sides by b:
[tex]\implies \dfrac{1 \cdot b}{b}=\dfrac{9 \cdot b}{b}-3b[/tex]
[tex]\implies 1=9-3b[/tex]
Add 3b to both sides:
[tex]\implies 1+3b=9-3b+3b[/tex]
[tex]\implies 3b+1=9[/tex]
Subtract 1 from both sides:
[tex]\implies 3b+1-1=9-1[/tex]
[tex]\implies 3b=8[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{3b}{3}=\dfrac{8}{3}[/tex]
[tex]\implies b=\dfrac{8}{3}[/tex]
