Question

complete the process of solving the equation. fill in the missing term on each line. simplify any fractions. 4(13c + 5) = 6c + 20 68c + \square = 6c + 20 apply the distributive property \square + 20 = 20 subtract 6c from both sides 62c = \square subtract 20 from both sides c = \square divide both sides by 62

Explanation:

Step1: Apply distributive property

The distributive property states that \(a(b + c)=ab+ac\). For \(4(13c + 5)\), we have \(4\times13c+4\times5 = 52c+20\)? Wait, wait, there is a typo in the original equation? Wait, the original equation is \(4(13c + 5)=6c + 20\)? Wait, no, the first line after the equation is \(68c+\square=6c + 20\)? Wait, maybe it's a typo, maybe the original coefficient is \(17\) instead of \(13\)? Because \(4\times17c=68c\). Let's assume that the original equation is \(4(17c + 5)=6c + 20\). Then by distributive property, \(4\times17c+4\times5=68c + 20\). So the first missing term is \(20\).

Step2: Subtract \(6c\) from both sides

Starting from \(68c + 20=6c + 20\), subtract \(6c\) from both sides: \((68c-6c)+20=(6c - 6c)+20\), which simplifies to \(62c+20 = 20\). So the second missing term is \(62c\).

Step3: Subtract \(20\) from both sides

Starting from \(62c+20 = 20\), subtract \(20\) from both sides: \(62c+(20 - 20)=20 - 20\), which simplifies to \(62c=0\). So the third missing term is \(0\).

Step4: Divide both sides by \(62\)

Starting from \(62c = 0\), divide both sides by \(62\): \(c=\frac{0}{62}=0\). So the fourth missing term is \(0\).

Answer:

First missing term: \(20\), Second missing term: \(62c\), Third missing term: \(0\), Fourth missing term: \(0\)