Properties of Arithmetic: Distributive Property

Algebra Level 1

What is the coefficient of x x after you simplify the expression :

5 ( 19 x + 2 ) + 2 ( 3 x + 5 ) ? 5 ( 19 x + 2) + 2 (3x + 5) ?

95 97 99 101

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3 solutions

Brilliant Mathematics Staff
Aug 1, 2020

5 ( 19 x + 2 ) + 2 ( 3 x + 5 ) = 5 × 19 x + 5 × 2 + 2 × 3 x + 2 × 5 = 95 x + 10 + 6 x + 10 = 101 x + 20 \begin{aligned} 5 (19 x + 2) + 2( 3x + 5) & = 5 \times 19 x + 5 \times 2 + 2 \times 3 x + 2 \times 5\\ & = 95x + 10 + 6x + 10 \\ & = 101 x + 20 \\ \end{aligned}

Hence, the coefficient of x x is 101.

2 Helpful 0 Interesting 1 Brilliant 0 Confused

Why is there +3, where it comes from. also what happens with the 20 at the end

Zerklyn Pertuz - 1 month, 2 weeks ago

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You're right, I've removed the +3 from my solution.

The question only cares about the coefficient of x x , (in this case, it's 101). So the constant of 20 is not important.

Brilliant Mathematics Staff - 1 month, 2 weeks ago
Mahdi Raza
Aug 3, 2020
  • The terms involving x x will be the only terms constituting for the final coefficient

5 ( 19 x + 2 ) + 2 ( 3 x + 5 ) ⟹ ( 5 × 19 ) + ( 2 × 3 ) = 101 5({\green{19x}} + 2) + 2({\green{3x}} + 5) \implies (5\times {\green{19}}) + (2 \times {\green{3}}) = \boxed{101}

0 Helpful 1 Interesting 1 Brilliant 1 Confused
Yajat Shamji
Aug 1, 2020

( 5 × 19 ) + ( 2 × 3 ) = 95 + 6 = 101 (5 \times 19) + (2 \times 3) = 95 + 6 = \fbox{101}

0 Helpful 0 Interesting 1 Brilliant 0 Confused

What happen with the 2 or 5, in those term ?

Zerklyn Pertuz - 1 month, 2 weeks ago

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