b.) \( 3(2 x+5)-(4 x+6)=19 \)

To solve the equation \( 3(2 x+5)-(4 x+6)=19 \), start by distributing the \(3\) across the first term: \( 3 \times 2x + 3 \times 5 = 6x + 15 \). Then tackle the subtraction: \( -(4x + 6) = -4x - 6 \). Now, combine all terms: \( 6x + 15 - 4x - 6 = 19 \). This simplifies to \( (6x - 4x) + (15 - 6) = 19 \), or \( 2x + 9 = 19 \). Next, subtract \(9\) from both sides to isolate the term with \(x\): \( 2x = 10 \), and finally, divide by \(2\) to find \(x = 5\). Check your work by substituting \(x = 5\) back into the original equation and confirming both sides equal \(19\).