Question

Twice the sum of a number and ten is equal to the difference of the number and
one half.

Answer 1

Answer:

What is the number, if the sum of twice a number and half the number is 10?

Let x be the unknown number.

2x + x/2 = 10 Given

2(2x) + 2(x/2) = 2(10) Multiply both side by 2

4x + x = 20 Multiplication

5x = 20 Combine like terms

(5x)/5 = (20)/5 Divide both sides by 5

x = 4

Check:

2x + x/2 = 10 Given

2(4) +(4)/2 = 10 ? Substitute 4 for x

8 + 2 = 10 ? Multiplication and Division

10 = 10 Addition

Answer: The number is 4 if the sum of twice the number and half the number is 10.

Have A Happy Day :-)

Answer 2

Given: Twice the sum of a number and ten is equal to the difference of the number and one half.

TO find:

the number

Solution:

Assume that the number is x.

Form the equation according to the conditions given in the question,

$\[2\left( {x + 10} \right) = x - \frac{1}{2}\]$

$\[ \Rightarrow 2x + 20 = \frac{{2x - 1}}{2}\]$

$\[\begin{array}{l} \Rightarrow 2\left( {2x + 20} \right) = 2x - 1\\ \Rightarrow 4x + 40 = 2x - 1\\ \Rightarrow 4x - 2x = - 40 - 1\\ \Rightarrow 2x = - 41\end{array}\]$

$\[ \Rightarrow x = - \frac{{41}}{2}\]$

Therefore, the number is $-\frac{41}{2}$.