Question

$$6 ( 3 x + 2 ) - 5 ( 6 x - 1 ) = 3 ( x - 8 ) - 5 ( 7 x - 6 ) + 9 x$$

Answer

x=11/115

Solution


Simplify  \(9x\times 15\)  to  \(135x\).
\[6(3x+2)-5(6x-1)=3(x-8)-5(7x-6)+135x\]
Expand.
\[18x+12-30x+5=3x-24-35x+30+135x\]
Simplify  \(18x+12-30x+5\)  to  \(-12x+17\).
\[-12x+17=3x-24-35x+30+135x\]
Simplify  \(3x-24-35x+30+135x\)  to  \(103x+6\).
\[-12x+17=103x+6\]
Add \(12x\) to both sides.
\[17=103x+6+12x\]
Simplify  \(103x+6+12x\)  to  \(115x+6\).
\[17=115x+6\]
Subtract \(6\) from both sides.
\[17-6=115x\]
Simplify  \(17-6\)  to  \(11\).
\[11=115x\]
Divide both sides by \(115\).
\[\frac{11}{115}=x\]
Switch sides.
\[x=\frac{11}{115}\]

Decimal Form: 0.095652