Question

what should be the first two steps to solve this equation? 2x +4(3x + 6) = 90 combine 2x and 3x and then distribute the 4. combine 2x and 3x and then subtract 6 from both sides subtract 6 from both sides and then divide by 4 distribute the 4 and then combine like terms by addition

Explanation:

Step1: Analyze the equation structure

The equation is \(2x + 4(3x + 6)=90\). The first step in solving linear equations with parentheses is usually to distribute the number outside the parentheses (the 4 here) to the terms inside. So we distribute 4: \(4\times3x + 4\times6=12x + 24\), so the equation becomes \(2x+12x + 24 = 90\).

Step2: Combine like terms

After distributing, we have like terms (the \(x\)-terms: \(2x\) and \(12x\)). Combining them: \(2x+12x=(2 + 12)x = 14x\), so the equation is now \(14x+24 = 90\). Looking at the options, the fourth option says "distribute the 4 and then combine like terms by addition" which matches these two steps. The other options have incorrect first steps (e.g., combining \(2x\) and \(3x\) first is wrong because \(3x\) is inside the parentheses and we need to distribute first, subtracting 6 first is wrong as we haven't distributed or combined like terms properly yet).

Answer:

The correct option is the fourth one: "distribute the 4 and then combine like terms by addition" (the right - most blue box option).