Question

1. 2(3x + 4) + 6x + 3 = 23

Explanation:

Step1: Expand the bracket

Using the distributive property \(a(b + c)=ab+ac\), we expand \(2(3x + 4)\) to get \(6x+8\). So the equation becomes \(6x + 8+6x + 3=23\).

Step2: Combine like terms

Combine the \(x\)-terms and the constant terms. The \(x\)-terms: \(6x+6x = 12x\), and the constant terms: \(8 + 3=11\). So the equation is now \(12x+11 = 23\).

Step3: Subtract 11 from both sides

Subtract 11 from each side of the equation: \(12x+11-11=23 - 11\), which simplifies to \(12x=12\).

Step4: Divide both sides by 12

Divide both sides by 12: \(\frac{12x}{12}=\frac{12}{12}\), so \(x = 1\).

Answer:

\(x = 1\)