Answer:
We conclude that:
[tex]\frac{18p}{5}+12q+18-\frac{18p}{5}-16q-6=-4q+12[/tex]
Hence, option A is true.
Step-by-step explanation:
Given the expression
[tex]3\left(\frac{6}{5}p+4q+6\right)-2\left(\frac{9}{5}p+8q+3\right)[/tex]
solving the expression
[tex]3\left(\frac{6}{5}p\:+\:4q\:+\:6\right)\:-\:2\left(\frac{9}{5}p\:+\:8q\:+\:3\right)=3\left(\frac{6p}{5}+4q+6\right)-2\left(\frac{9p}{5}+8q+3\right)[/tex]
Expand [tex]3\left(\frac{6p}{5}+4q+6\right)=\frac{18p}{5}+12q+18[/tex]
[tex]=\frac{18p}{5}+12q+18-2\left(\frac{9p}{5}+8q+3\right)[/tex]
Expand [tex]-2\left(\frac{9p}{5}+8q+3\right)=-\frac{18p}{5}-16q-6[/tex]
[tex]=\frac{18p}{5}+12q+18-\frac{18p}{5}-16q-6[/tex]
Group like terms:
[tex]=\frac{18p}{5}-\frac{18p}{5}+12q-16q+18-6[/tex]
Add similar elements: [tex]\frac{18p}{5}-\frac{18p}{5}=0[/tex]
[tex]=12q-16q+18-6[/tex]
Add similar elements: 12q-16q=-4q
[tex]=-4q+18-6[/tex]
[tex]=-4q+12[/tex]
Therefore, we conclude that:
[tex]\frac{18p}{5}+12q+18-\frac{18p}{5}-16q-6=-4q+12[/tex]
Hence, option A is true.
