If I am reading the question correctly it would come out to -6x+42 First do all the addition and squaring, then factor in that negative. You come out to -2x^3 +2x^3-4x-2x+25+5+9+3. The x^3's cancel, the -x's add to -6x, then all that other adds to 42.
Multiply the 3 times 4. Then do the same on the top.
Laura's age is 9 years.
Solution:
Let x be the age of April.
Laura's age = 2 years more than half of April's age
<u>Convert statement into algebraic expression:</u>
Half of April's age = ![\frac{x}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D)
2 years more than half of April's age = ![\frac{x}{2}+2](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D%2B2)
Combined age of April and Laura = 23
⇒ April's age + Laura's age = 23
![$\Rightarrow \ \ x+(\frac{x}{2}+2) =23](https://tex.z-dn.net/?f=%24%5CRightarrow%20%5C%20%5C%20x%2B%28%5Cfrac%7Bx%7D%7B2%7D%2B2%29%20%3D23)
![$\Rightarrow \ \ x+\frac{x}{2}+2 =23](https://tex.z-dn.net/?f=%24%5CRightarrow%20%5C%20%5C%20x%2B%5Cfrac%7Bx%7D%7B2%7D%2B2%20%3D23)
![$\Rightarrow \ \ \frac{x}{1}+\frac{x}{2}+\frac{2}{1} =23](https://tex.z-dn.net/?f=%24%5CRightarrow%20%5C%20%5C%20%5Cfrac%7Bx%7D%7B1%7D%2B%5Cfrac%7Bx%7D%7B2%7D%2B%5Cfrac%7B2%7D%7B1%7D%20%3D23)
To add the fractions make the denominators same.
Multiplying 2 on both numerator and denominator of unlike terms, we get
![$\Rightarrow \ \ \frac{x\times2}{1\times2}+\frac{x}{2}+\frac{2\times2}{1\times2} =23](https://tex.z-dn.net/?f=%24%5CRightarrow%20%5C%20%5C%20%5Cfrac%7Bx%5Ctimes2%7D%7B1%5Ctimes2%7D%2B%5Cfrac%7Bx%7D%7B2%7D%2B%5Cfrac%7B2%5Ctimes2%7D%7B1%5Ctimes2%7D%20%3D23)
![$\Rightarrow \ \ \frac{2x}{2}+\frac{x}{2}+\frac{4}{2} =23](https://tex.z-dn.net/?f=%24%5CRightarrow%20%5C%20%5C%20%5Cfrac%7B2x%7D%7B2%7D%2B%5Cfrac%7Bx%7D%7B2%7D%2B%5Cfrac%7B4%7D%7B2%7D%20%3D23)
Denominators are same, now add the fractions.
![$\Rightarrow \ \ \frac{2x+x+4}{2} =23](https://tex.z-dn.net/?f=%24%5CRightarrow%20%5C%20%5C%20%5Cfrac%7B2x%2Bx%2B4%7D%7B2%7D%20%3D23)
Do cross multiplication.
![$\Rightarrow \ \ 2x+x+4=23\times2](https://tex.z-dn.net/?f=%24%5CRightarrow%20%5C%20%5C%202x%2Bx%2B4%3D23%5Ctimes2)
![$\Rightarrow \ \ 3x=46-4](https://tex.z-dn.net/?f=%24%5CRightarrow%20%5C%20%5C%203x%3D46-4)
![$\Rightarrow \ \ 3x=42](https://tex.z-dn.net/?f=%24%5CRightarrow%20%5C%20%5C%203x%3D42)
![$\Rightarrow \ \ x=14](https://tex.z-dn.net/?f=%24%5CRightarrow%20%5C%20%5C%20x%3D14)
Aprils's age = 14 years
Laura's age = ![\frac{14}{2}+2](https://tex.z-dn.net/?f=%5Cfrac%7B14%7D%7B2%7D%2B2)
= 7 + 2
Laura's age = 9
Hence Laura's age is 9 years.