Simplify the expressions and find the value if $x$ is equal to $2$
$(i)$. $x+7+4(x-5)$
$(ii)$. $3(x+2)+5x-7$
$(iii)$. $6x+5(x-2)$
$(iv)$. $4(2x-1)+3x+11$
Given: $(i)$. $x+7+4(x-5)$
$(ii)$. $3(x+2)+5x-7$
$(iii)$. $6x+5(x-2)$
$(iv)$. $4(2x-1)+3x+11$
To do: To simplify the expressions and find the value of $x$ is equal to $2$.
Solution:
$(i)$. $x+7+4(x-5)$
$=x+7+4x-20$
$=x+4x+7-20$
$=5x+7-20$
$=5x-13$
$=5(2)-13$ If, $x=2$
$=10-13$
$=-3$
$(ii)$. $3(x+2)+5x-7$
$=3x+6+5x-7$
$=8x-1$
$=8(2) - 1$ If, $x=2$
$=16 - 1$
$=15$
$iii)$. $6x+5(x-2)$
$=6x+5x-10$
$=11x-10$
$=11(2)-10$ If, $x=2$
$=22-10$
$=12$
$(iv)$. $4(2x-1)+3x+11$
$=8x-4+3x+11$
$=11x+7$
$=11(2) +7$ If, $x=2$
$=22+7$
$=29$
Related Articles
- Factorise:(i) \( 12 x^{2}-7 x+1 \)(ii) \( 2 x^{2}+7 x+3 \)(iii) \( 6 x^{2}+5 x-6 \)(iv) \( 3 x^{2}-x-4 \)
- Simplify the following :$( 3 x^2 + 5 x - 7 ) (x-1) - ( x^2 - 2 x + 3 ) (x + 4)$
- Find the value of the following expressions, when $x=-1$$(i)$. $2x-7$$(ii)$. $-x+2$$(iii)$. $x^2+2x+ 1$$(iv)$. $2x^2-x-2$
- Find the following products:(i) $(x + 4) (x + 7)$(ii) $(x - 11) (x + 4)$(iii) $(x + 7) (x - 5)$(iv) $(x - 3) (x - 2)$(v) $(y^2 - 4) (y^2 - 3)$(vi) $(x + \frac{4}{3}) (x + \frac{3}{4})$(vii) $(3x + 5) (3x + 11)$(viii) $(2x^2 - 3) (2x^2 + 5)$(ix) $(z^2 + 2) (z^2 - 3)$(x) $(3x - 4y) (2x - 4y)$(xi) $(3x^2 - 4xy) (3x^2 - 3xy)$(xii) $(x + \frac{1}{5}) (x + 5)$(xiii) $(z + \frac{3}{4}) (z + \frac{4}{3})$(xiv) $(x^2 + 4) (x^2 + 9)$(xv) $(y^2 + 12) (y^2 + 6)$(xvi) $(y^2 + \frac{5}{7}) (y^2 - \frac{14}{5})$(xvii) $(p^2 + 16) (p^2 - \frac{1}{4})$
- Simplify:$(x^3 - 2x^2 + 3x - 4) (x - 1) - (2x - 3) (x^2 - x + 1)$
- Describe how the following expressions are obtained:$(i) 7 x y+5, (ii) x^{2} y, (iii) 4 x^{2}-5 x$.
- Simplify:Â $( 3x\ +\ 4)( 2x\ -\ 3) \ +\ ( 5x\ -\ 4)( x\ +\ 2)$
- Find the value of the polynomial \( 5 x-4 x^{2}+3 \) at(i) \( x=0 \)(ii) \( x=-1 \)(iii) \( x=2 \)
- Write the degree of each of the following polynomials:(i) \( 5 x^{3}+4 x^{2}+7 x \)(ii) \( 4-y^{2} \)(iii) \( 5 t-\sqrt{7} \)(iv) 3
- Divide the polynomial $p(x)$ by the polynomial $g(x)$ and find the quotient and remainder, in each of the following:(i) $p(x) = x^3 - 3x^2 + 5x -3, g(x) = x^2-2$(ii) $p(x) =x^4 - 3x^2 + 4x + 5, g(x) = x^2 + 1 -x$(iii) $p(x) = x^4 - 5x + 6, g(x) = 2 -x^2$
- \Find $(x +y) \div (x - y)$. if,(i) \( x=\frac{2}{3}, y=\frac{3}{2} \)(ii) \( x=\frac{2}{5}, y=\frac{1}{2} \)(iii) \( x=\frac{5}{4}, y=\frac{-1}{3} \)(iv) \( x=\frac{2}{7}, y=\frac{4}{3} \)(v) \( x=\frac{1}{4}, y=\frac{3}{2} \)
- Add the following algebraic expressions(i) \( 3 a^{2} b,-4 a^{2} b, 9 a^{2} b \)(ii) \( \frac{2}{3} a, \frac{3}{5} a,-\frac{6}{5} a \)(iii) \( 4 x y^{2}-7 x^{2} y, 12 x^{2} y-6 x y^{2},-3 x^{2} y+5 x y^{2} \)(iv) \( \frac{3}{2} a-\frac{5}{4} b+\frac{2}{5} c, \frac{2}{3} a-\frac{7}{2} b+\frac{7}{2} c, \frac{5}{3} a+ \) \( \frac{5}{2} b-\frac{5}{4} c \)(v) \( \frac{11}{2} x y+\frac{12}{5} y+\frac{13}{7} x,-\frac{11}{2} y-\frac{12}{5} x-\frac{13}{7} x y \)(vi) \( \frac{7}{2} x^{3}-\frac{1}{2} x^{2}+\frac{5}{3}, \frac{3}{2} x^{3}+\frac{7}{4} x^{2}-x+\frac{1}{3} \) \( \frac{3}{2} x^{2}-\frac{5}{2} x-2 \)
- Which of the following expressions are not polynomials?:(i) $x^2+2x^{-2}$(ii) $\sqrt{ax}+x^2-x^3$(iii) $3y^3-\sqrt{5}y+9$(iv) $ax^{\frac{1}{2}}y^7+ax+9x^2+4$(v) $3x^{-3}+2x^{-1}+4x+5$
- Simplify the following:$(3x+4)(2x-3)+(5x-4)(x+2)$.
- Simplify:$(x^2-3x + 2) (5x- 2) - (3x^2 + 4x-5) (2x- 1)$
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies