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[tex]\qquad \sf  \dashrightarrow \: \cfrac{1}{b} + 10 = \cfrac{9}{b} + 7[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{9}{b} - \cfrac{1}{b} = 10 - 7[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{8}{b} = 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: b = \cfrac{8}{3} [/tex]

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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]

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