Answer :
First you subtract 7 minus 19 and 7/8b minus 5/4b:
5/4b+7=7/8b+19
-7/8b -7/8b
5/4b+7=7/8b+19
-7 -7
3/8b=12
Then you divide 12 by 3/8:
b=32
5/4b+7=7/8b+19
-7/8b -7/8b
5/4b+7=7/8b+19
-7 -7
3/8b=12
Then you divide 12 by 3/8:
b=32
[tex]\mathrm{Subtract\:}7\mathrm{\:from\:both\:sides} \ \textgreater \ \frac{5}{4}b+7-7=\frac{7}{8}b+19-7 \ \textgreater \ Simplify[/tex]
[tex]\frac{5}{4}b+7-7 \ \textgreater \ \mathrm{Add\:similar\:elements:}\:7-7=0 \ \textgreater \ \frac{5}{4}b[/tex]
[tex]\frac{7}{8}b+19-7 \ \textgreater \ \mathrm{Add/Subtract\:the\:numbers:}\:19-7=12 \ \textgreater \ \frac{7}{8}b+12[/tex]
[tex]\frac{5}{4}b=\frac{7}{8}b+12[/tex]
[tex]\mathrm{Subtract\:}\frac{7}{8}b\mathrm{\:from\:both\:sides} \ \textgreater \ \frac{5}{4}b-\frac{7}{8}b=\frac{7}{8}b+12-\frac{7}{8}b \ \textgreater \ Simplify[/tex]
[tex]\frac{5}{4}b-\frac{7}{8}b \ \textgreater \ \mathrm{Factor\:out\:common\:term\:}b\ \textgreater \ b\left(\frac{5}{4}-\frac{7}{8}\right)[/tex]
[tex]\frac{5}{4}-\frac{7}{8} \ \textgreater \ \mathrm{Factor\:each\:denominator\:into\:its\:primes} \ \textgreater \ 4=2^2 \ \textgreater \ 8=2^3[/tex]
[tex]\mathrm{Find\:the\:least\:common\:denominator\:}2^3=8[/tex]
[tex]\mathrm{Adjust\:Fractions\:based\:on\:the\:LCD} \ \textgreater \ \frac{5\cdot \:2}{8}-\frac{7}{8}[/tex]
[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}: \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]
[tex]\frac{2\cdot \:5-7}{8} \ \textgreater \ \mathrm{Multiply\:the\:numbers:}\:2\cdot \:5=10 \ \textgreater \ 10-7 \ \textgreater \ 3\ \textgreater \ \frac{3}{8}[/tex]
[tex]\frac{3}{8}b[/tex]
[tex]\frac{7}{8}b+12-\frac{7}{8}b \ \textgreater \ \mathrm{Add\:similar\:elements:}\:\frac{7}{8}b-\frac{7}{8}b=0 \ \textgreater \ 12 \ \textgreater \ \frac{3}{8}b=12[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}8 \ \textgreater \ 8\cdot \frac{3}{8}b=12\cdot \:8 \ \textgreater \ \mathrm{Simplify} \ \textgreater \ 3b=96[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}3 \ \textgreater \ \frac{3b}{3}=\frac{96}{3} \ \textgreater \ Simplify \ \textgreater \ b=32[/tex]
Hope this helps!
[tex]\frac{5}{4}b+7-7 \ \textgreater \ \mathrm{Add\:similar\:elements:}\:7-7=0 \ \textgreater \ \frac{5}{4}b[/tex]
[tex]\frac{7}{8}b+19-7 \ \textgreater \ \mathrm{Add/Subtract\:the\:numbers:}\:19-7=12 \ \textgreater \ \frac{7}{8}b+12[/tex]
[tex]\frac{5}{4}b=\frac{7}{8}b+12[/tex]
[tex]\mathrm{Subtract\:}\frac{7}{8}b\mathrm{\:from\:both\:sides} \ \textgreater \ \frac{5}{4}b-\frac{7}{8}b=\frac{7}{8}b+12-\frac{7}{8}b \ \textgreater \ Simplify[/tex]
[tex]\frac{5}{4}b-\frac{7}{8}b \ \textgreater \ \mathrm{Factor\:out\:common\:term\:}b\ \textgreater \ b\left(\frac{5}{4}-\frac{7}{8}\right)[/tex]
[tex]\frac{5}{4}-\frac{7}{8} \ \textgreater \ \mathrm{Factor\:each\:denominator\:into\:its\:primes} \ \textgreater \ 4=2^2 \ \textgreater \ 8=2^3[/tex]
[tex]\mathrm{Find\:the\:least\:common\:denominator\:}2^3=8[/tex]
[tex]\mathrm{Adjust\:Fractions\:based\:on\:the\:LCD} \ \textgreater \ \frac{5\cdot \:2}{8}-\frac{7}{8}[/tex]
[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}: \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]
[tex]\frac{2\cdot \:5-7}{8} \ \textgreater \ \mathrm{Multiply\:the\:numbers:}\:2\cdot \:5=10 \ \textgreater \ 10-7 \ \textgreater \ 3\ \textgreater \ \frac{3}{8}[/tex]
[tex]\frac{3}{8}b[/tex]
[tex]\frac{7}{8}b+12-\frac{7}{8}b \ \textgreater \ \mathrm{Add\:similar\:elements:}\:\frac{7}{8}b-\frac{7}{8}b=0 \ \textgreater \ 12 \ \textgreater \ \frac{3}{8}b=12[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}8 \ \textgreater \ 8\cdot \frac{3}{8}b=12\cdot \:8 \ \textgreater \ \mathrm{Simplify} \ \textgreater \ 3b=96[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}3 \ \textgreater \ \frac{3b}{3}=\frac{96}{3} \ \textgreater \ Simplify \ \textgreater \ b=32[/tex]
Hope this helps!