rewrite! Write an new and equivalent equation that is easier to solve

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[tex] \sf 7( \sqrt{m + 1} - 3) = 21[/tex]

we will multiply 7 with bracket

[tex] \sf 7 \sqrt{m + 1} - 21 = 21[/tex]

Now we will take (-21) on LHS to RHS

[tex] \sf 7 \sqrt{m + 1} = 21 + 21 \\ \\ \sf7 \sqrt{m + 1 } = 42 \\ \\ \sf \sqrt{m + 1} = \frac{42}{7} \\ \\ \sf \sqrt{m + 1} = 6[/tex]

Now we will do squaring both sides

[tex] \sf {( \sqrt{m + 1}) }^{2} = {(6)}^{2} \\ \\ \sf \red {m + 1 = 36}[/tex]

[tex]\sf{ 7( \sqrt{m+1} - 3)=21}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\sf{\sqrt{m+1} - 3)=\frac{21}{7}}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\sf{ 7( \sqrt{m+1} - 3)=3}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\sf{\sqrt{m+1} =6}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Get the power of 2 in both sides.

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\sf{( \sqrt{m + 1})^2 = 6^2}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\sf{m+1=36}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\sf{m=35}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

So the answer is m = 35

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