Question

How do you simplify 5(3.4k – 7) + (3k + 21)?

Answer 1

Hint: We are given an expression as 5(3.4k – 7) + (3k + 21). To solve and simplify this we will learn how we should multiply and divide and how we add the term. We will learn what terms can be added and which cannot be. Then we first multiply and then add the like terms and simplify the term by term and get our answer.

Complete step by step answer:
We are given an expression as 5(3.4k – 7) + (3k + 21). We can see that we are given the expression a single variable and the variable power is just 1, so this expression is linear. Now when we simplify our problem, we should remember that only like terms can be added or subtracted. Like term means the terms with the same type that is the variable added to the variable terms, constantly added to constant. For example, 3x + 2x = 5x, 2 + 3 = 5. We cannot add 3 + 2x = 5x as 3 is a constant and 2x is term with variable. So, they cannot be added up. Similarly, we cannot subtract such terms as well. While we multiply any single term with the constant, we will always multiply each term of the bracket with that term. Now using this knowledge, we solve and simplify our given problem. We have
\[5\left( 3.4k-7 \right)+\left( 3k+21 \right)\]
Opening the first bracket, we get,
\[\Rightarrow 5\times 3.4k+5\times \left( -7 \right)+\left( 3k+21 \right)\]
On simplifying, we get,
\[\Rightarrow 17k-35+3k+21\]
Now, we add the like terms. So, we get,
\[\Rightarrow 17k+3k-35+21\]
So, we get,
\[\Rightarrow 20k-14\]
So, we get our 5(3.4k – 7) + (3k + 21) term simplified as 20k – 14.

Note:
 We can cross-check if our given equation is correctly simplified or not. We will use the value of k and solve each equation and check that they are given the same solution or not. We will let k = 1, so putting k = 1 in 5(3.4k – 7) + (3k + 21), we get,
\[\Rightarrow 5\left( 3.4-7 \right)+\left( 3+21 \right)\]
\[\Rightarrow 5\left( -3.6 \right)+24\]
So, we get 6. Now, putting k = 1 in 20k – 14, we get,
\[\Rightarrow 20\times 1-14\]
\[\Rightarrow 20-14\]
\[\Rightarrow 6\]
Both are the same. So, the solution is correct.