Question

select the term that would make the equation true:
$5(3x - 4) = \square - 20$
$3x - \square = 3(x - 7)$
$\square (3y + 9) = 12y + 36$

Explanation:

Step1: Solve the first equation \(5(3x - 4)=\square - 20\)

Use the distributive property \(a(b - c)=ab - ac\) on the left side.
\(5\times3x-5\times4 = 15x-20\)
So the missing term is \(15x\).

Step2: Solve the second equation \(3x-\square = 3(x - 7)\)

First, simplify the right side using the distributive property.
\(3(x - 7)=3x-3\times7 = 3x - 21\)
Now, the equation is \(3x-\square=3x - 21\). Subtract \(3x\) from both sides, we get \(-\square=-21\), so \(\square = 21\).

Step3: Solve the third equation \(\square(3y + 9)=12y + 36\)

Factor the right side: \(12y+36 = 12(y + 3)=4\times3(y + 3)=4(3y + 9)\) (since \(3y+9 = 3(y + 3)\), and \(12y+36=4\times3y+4\times9\)).
So the missing term is \(4\).

Answer:

First equation: \(15x\)
Second equation: \(21\)
Third equation: \(4\)