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How do you simplify #2[3(3x +1)+ 2( 2x +5)] + 3[1+ 4(x+2)+5x]#?

Answer 1

Eli Assouline

#53x+53#

Notice that there are 2 terms. Start my removing the brackets within each term using the distributive law

#color(red)(2[3(3x +1)+ 2( 2x +5)] )+ color(blue)(3([1+ 4(x+2)+5x]#

=#color(red)(2[9x +3+ 4x +10)] + color(blue)(3[1+ 4x+8+5x]" "larr#simplify

=#color(red)(2[13x +13)] + color(blue)(3[9x+9])" "larr#remove brackets

=#26x+26 +27x+27" "larr# simplify

=#53x +53#

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Answer 2

Julia Adams

To simplify the expression 2[3(3x + 1) + 2(2x + 5)] + 3[1 + 4(x + 2) + 5x], follow the order of operations (PEMDAS/BODMAS):

Step 1: Simplify the expressions within the innermost parentheses. 3(3x + 1) = 9x + 3 2(2x + 5) = 4x + 10 4(x + 2) = 4x + 8

Step 2: Simplify the expressions within the brackets. 2[9x + 3 + 4x + 10] = 2[13x + 13] 3[1 + 4x + 8 + 5x] = 3[9x + 9]

Step 3: Simplify the expressions within the outermost brackets. 2[13x + 13] = 26x + 26 3[9x + 9] = 27x + 27

Step 4: Combine like terms. 26x + 26 + 27x + 27 = 53x + 53

Therefore, the simplified expression is 53x + 53.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.