Option B, C, E
2(x +3) + 2x and 4x +3 are not equal
(5x+1) +6 and 5x +5 are not equal
4 + 5(x - 2) and 3x + 4 are not equal
<em><u>Solution:</u></em>
We have to find the pair of expressions that are equal
<h3><u>Option A</u></h3>3(x+2) + 4x and 7x+6
Let us simplify the first expression
First expression : 3(x + 2) + 4x
By distributive property, we know that,
a(b + c) = ab + ac
Applying this we get,
3(x + 2) + 4x = 3x + 6 + 4x = 7x + 6
Thus the first and second expressions are equal
<h3><u>Option B</u></h3>2(x +3) + 2x and 4x +3
Let us simplify the first expression
First expression : 2(x + 3) + 2x
Similarly using distributive property,
2(x + 3) + 2x = 2x + 6 + 2x = 4x + 6
Thus first and second expressions are not equal
<h3><u>Option C</u></h3>(5x+1) +6 and 5x +5
Let us simplify the first expression
First expression : (5x + 1) + 6
Remove the parenthesis we get,
(5x + 1) + 6 = 5x + 1 + 6 = 5x + 7
Thus first and second expressions are not equal
<h3><u>Option D</u></h3>8 + 4(x + 1) and 4x + 12
Let us simplify the first expression
First expression : 8 + 4(x + 1)
Similarly using distributive property,
8 + 4(x + 1) = 8 + 4x + 4 = 4x + 12
Thus first and second expressions are equal
<h3><u>Option E</u></h3>4 + 5(x - 2) and 3x + 4
Let us simplify the first expression
First expression : 4 + 5(x - 2)
Similarly using distributive property,
4 + 5(x - 2) = 4 + 5x - 10 = 5x - 6
Thus first and second expressions are not equal