From the question it is given that, $(x+3)/3\le (x+8)/4$ So, by cross multiplication we get, $4(x+3)\le 3(x+8)$ $4x+12\le 3x+24$ Now, transposing we get $4x-3x\le 24-12$ $x\le 12$ As per the...
Solve for$x:7+5x>x-13$, where x is a negative integer.
From the question it is given that, $7+5x>x-13$ So, by transposing we get, $5x-x>-13-7$ $4x>-20$ $x>-20/4$ $x>-5$ As per the condition given in the question, x is a negative integer....
Solve for $x:3-2x\ge -12,x\in N$
From the question it is given that, $3-2x\ge x-12$ So, by transposing we get, $2x+x\le 12+3$ $3x\le 15$ $3x\le 15$ $x\le 15/3$ $x\le 5$ As per the condition given in the question$x\in N$ Therefore,...
Solve for $x:6-10x<36,x\in \left\{ -3,-2,-1,0,1,2 \right\}$
From the question it is given that, $6-10x<36$ So, by transposing we get, $-10x<36-6$ $-10x<30$ $10x>-30$ $x>-30/10$ $x>-3$ As per the condition given in the question, $x\in...
Solve for x in the following in equations, if the replacement set is N<10: (v) $5-2x<11$
Solution: - $5-2x<11$ By transposing we get, $2x>511$ $2x>-6$ $x>-6/2$ $x>-3$ As per the condition given in the question, $\left\{ x:x\in N;N<10 \right\}$ Therefore, solution set...
Solve for x in the following in equations, if the replacement set is N<10: (iii) $3x-5\le 7$ (iv) $8-3x\ge 2$
Solution: - $3x-5\le 7$ By transposing we get, $3x-5\le 7$ $x\le 12/3$ $x\le 4$ As per the condition given in the question, $\left\{ x:x\in N;N<10 \right\}$ Therefore, solution set $x=\left\{...
Solve for x in the following in equations, if (i) $x+5\ge 11$ (ii) $2x+1<17$
Solution: $x+5\ge 11$ By transposing we get, $x>115$ $x>6$ As per the condition given in the question $\left\{ x:x\in N;N<10 \right\}$ Therefore, solution $x=\left( 7,8,9 \right)$ Solution:...
Solve for x in the following in-equations, if the replacement set is R; (ix) $2x-7\ge 5x+8$ (x) $9-4x\le 15-7x$
Solution: - $2x-7\ge 5x+8$ By transposing we get, $5x-2x\le 8-7$ $3x\le -15$ $x\le 15/3$ $x\le -5$ As per the condition given in the question, the replacement set is R. Therefore, solution set...
Solve for x in the following in-equations, if the replacement set is R; (vii) $2\left( 3x-5 \right)\le 8$ (viii) $x+7\le 15+3x$
Solution: - $2\left( 3x-5 \right)\le 8$ $6x-10\le 8$ $6x\le 18$ $x\le 18/6$ $x\le 3$ By transposing we get, As per the condition given in the question, the replacement set is R. Therefore, solution...
Solve for x in the following in-equations, if the replacement set is R; (v) $7x+11>16-3x$ (vi) $3x+25>8x-10$
Solution: - $7x+11>16-3x$ By transposing we get, $7x+11>16-11$ $10x>5$ $x>5/10$ $x>0.5$ $x>1/2$ As per the condition given in the question, the replacement set is R. Therefore,...
Solve for x in the following in-equations, if the replacement set is R; (iii) $3x+2\le 11$ (iv) $14-3x\ge 5$
Solution: $3x+2\le 11$ By transposing we get, $3x+2\le 11$ $3x\le 11-2$ $3x\le 9$ $x\le 9/3$ $x\le 3$ As per the condition given in the question, the replacement set is R. Therefore, solution set...
Solve for x in the following in-equations, if the replacement set is R; (i) $3x\ge 12$ (ii) $2x-3\ge 7$
(i) $3x\ge 12$ By cross multiplication we get, $x\ge 12/3$ $x\ge 4$ As per the condition given in the question, the replacement set is R. Therefore, solution set $x=\left[ x:x\in R;x\ge 4 \right]$...
Solve for $x:3-2x\ge x-12,X\in N$
From the question it is given that, $3-2x\ge x-12$ So, by transposing we get, $2x+x\le 12+3$ $3x\le 15$ $x\le 15/3$ $x\le 5$ As per the condition given in the question, $x\in W$. Therefore, solution...
Solve for $x:5x-14<18-3x,x\in W$
An equation between two variables that gives a straight line when plotted on a graph. From the question it is given that, $5x+3x<18-3x$ So, by transposing we get, $5x+3x<18+14$ $8x<32$...
If$x+17\le 4x+9$, find the smallest value of x, when: (i) $x\in Z$ (ii) $x\in R$
(i) Solution: - From the question, $x+17\le 4x+9$ So, by transposing we get, $4x-x\ge 17-9$ $3x\ge 8$ $x\ge 8/3$ As per the condition given in the question, $x\in Z$ Therefore, smallest value of...
If $(2x+7)/3\le 3(5x+1)/4$, find the smallest value of x, when: (i) $x\in R$ (ii) $x\in Z$
(i) Solution: - From the question, $\left( 2x+7 \right)/3\le \left( 5x+1 \right)/4$ So, by cross multiplication we get, $4\left( 2x+7 \right)\le 3\left( 5x+1 \right)$ $8x+28\le 15x+3$ Now...
If $P=\left\{ x:7-4>5x+2,x\in R \right\}$ and $Q=\left\{ x:x-19\ge 1-3x,x\in R \right\}$, represent the following solution set on the different number lines: (i) $P\bigcap Q$
As per the condition given in the question, $P=\left\{ x:7x4>5x+2,x\in R \right\}$ $7x4>5x+2$ By transposing we get, $7x5x>4+2$ $2x>6$ $x>6/2$ $x>3$ Therefore, $P=\left\{...
Solve for$x:x/4+3\le x/3+4$, where x is a negative odd number.
From the question it is given that, $x/4+3\le x/3+4$ So, by transposing we get, $x/4-x/3\le 4-3$ $\left( 3x-4x \right)/12\le 1$ $-x\le 12$ $x\ge -12$ As per the condition given in the question, x is...
Solve for$x:2x+7\ge 5x-14$, where x is a positive prime number.
From the question it is given that, $2x+7\ge 5x-14$ So, by transposing we get, $5x-2x\le 14+7$ $3x\le 21$ $x\le 21/3$ $x\le 7$ As per the condition given in the question, x is a positive prime...
If $p=\left\{ x:3
$PQ=\left\{ -2,-1,0,1,2,3,4,5,6,7 \right\}\left\{ -7,-6,-5,-4,-3,-2,-1,0,1,2 \right\}=\left\{ 3,4,5,6,7 \right\}$
If $p=\left\{ x:-3
As per the condition given in the question, $p=\left\{ x:-3<x\le 7,x\in R \right\}$ So, $P=\left\{ -2,-1,0,1,2,3,4,5,6,7 \right\}$ Then, $Q=\left\{ x:-7\le x<3,x\in R \right\}$ $Q=\left\{...
Solve the following linear in-equations and graph the solution set on a real number line.(ix) $1/3\left( 5x-8 \right)\ge 1/2\left( 4x-7 \right),x\in R$(x) $5/4x>1+1/3\left( 4x-1 \right),X\in R$
Solution: - From the question it is given that, $1/3\left( 5x-8 \right)\ge 1/2\left( 4x7 \right)$ By cross multiplication we get, $2\left( 5x-8 \right)\ge 3\left( 4x7 \right)$ $10x16\ge 12x21$...
Solve the following linear in-equations and graph the solution set on a real number line.$4\frac{3}{4}\ge x+15/61/3,x\in R$(viii) $1/3\left( 2x-1 \right)<\left( x+5 \right)<1/6\left( 3x+4 \right),x\in R$
Solution:- From the question, Consider, $43/4\ge x+5/6$ $19/4\ge \left( 6x+5 \right)/6$ $114\ge 24x+20$ By transposing we get, $11420\ge...
Solve the following linear in-equations and graph the solution set on a real number line.(v) $2x-7<5x+2\le 3x+14,x\in R$(vi) $-3\le 1/2-(2\times /3)\le $$2\frac{2}{3}X\in N$
Solution:- From the question, Consider $2x-7<5x+2$ By transposing we get, $5x-2x>-7-2$ $3x<-9$ $x<-9/3$ $x<-3$ Now, consider $5x+2\le 3x+14$ So, by transposing we get, $5x-2x-14-2$...
Solve the following linear in-equations and graph the solution set on a real number line.(iii) $2\left( 3x-5 \right)>5\left( 13-2x \right),x\in W$(iv) $3x-9\le 4x-7<2x+5,x\in R$
From the question it is given that, $2(3x-5)>(13-2x)$$6x-10>65-10x$ So, by transposing we get, $6x+10x>65+10$ $16x>75$ $x>75/16$ $x>4\frac{11}{16}$ As per the condition given in...
Solve the following linear in-equations and graph the solution set on a real number line.(i)$2x-11\le 7-3x,x\in N$.(ii)$3(5x+3)\ge 2(9x-17),x\in W$.
$2x-11\le 7-3x,x\in N$ By transposing we get, $2x+3x\le 7+11$ $5x\le 18$ $5x\le 18/5$ $x\le 3.6$ As per the condition given in the question, $x\in N$ Therefore, solution set $x\in N$ Set can...
Solve for$x:x/4+3\le x/3+4$, where x is a negative odd number.
From the question it is given that, $x/4+3\le x/3+4$ So, by transposing we get, $x/4-x/3\le 4-3$ $(3x-4x)/12\le 1$ $-x\le 12$ $x\ge -12$ As per the condition given in the question, x is a negative...
Solve for$x:2x+7\ge 5x-14$, where x is a positive prime number.
From the question it is given that, $2x+7\ge 5x-14$ So, by transposing we get, $5x-2x\le 14+7$ $3x\le 21$ $x\le 21/3$ $x\le 7$ As per the condition given in the question, x is a positive prime...