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Algebra - Solving Inequalities with Unknowns on Both Sides

  a - answer    s - solution    v - video

Question 1


Solve the following, showing your solution on a number line

a) $2x>x+3$  a s v
b) $6x>5x+7$  a s v
c) $5+10x\le11x$  a s v
d) $29x+10\ge30x$  a s v
e) $12y-4>13y$  a s v
f) $-6z<16-7z$  a s v


Question 2


Solve the following, showing your solution on a number line

a) $3x\ge x+8$  a s v
b) $11x\ge4x-42$  a s v
c) $36-2x>4x$  a s v
d) $4m<19-15m$  a s v
e) $22-x\le 43x$  a s v
f) $11a\le -100-9a$  a s v


Question 3


Solve the following, showing your solution on a number line

a) $\frac{x+6}{3}\le x$  a s v
b) $\frac{30-4x}{2}\ge x$  a s v
c) $-12x> \frac{4x+100}{3}$  a s v


Question 4


Solve the following, showing your solution on a number line

a) $x+4\le2x+3$  a s v
b) $5x+7\ge4x+10$  a s v
c) $18x-5<17x+80$  a s v
d) $4-6x>9-7x$  a s v
e) $6-4a<8-3a$  a s v
f) $-12-16h<-17h-44$  a s v


Question 5


Solve the following, showing your solution on a number line

a) $15+5x\ge3x+25$  a s v
b) $20+7x\le10x+17$  a s v
c) $12x-3<19+20x$  a s v
d) $2w-25>8-9w$  a s v
e) $16-7n\le10-10n$  a s v
f) $8x+20>-9x-31$  a s v


Question 6


Solve the following, showing your solution on a number line

a) $2(x+4)\ge x+10$  a s v
b) $5(x+3)<4x+55$  a s v
c) $3(x-4)<2x$  a s v
d) $4+10x\ge9(x+3)$  a s v
e) $16-4x>5(4-x)$  a s v
f) $-8(x+6)\le20-7x$  a s v


Question 7


Solve the following, showing your solution on a number line

a) $5(x+1)>2x+14$  a s v
b) $6x+44>2(x+30)$  a s v
c) $3(x-3)\le11+5x$  a s v
d) $3(2x+10)\ge15x+3$  a s v
e) $5-7x\le-2(3-2x)$  a s v
f) $-5(12-4x)\ge-10x+90$  a s v


Question 8


Solve the following, showing your solution on a number line

a) $4(x+6)>5(x+2)$  a s v
b) $4(2x+3)\le7(x+5)$  a s v
c) $7(3x-3)>11(2x-4)$  a s v
d) $6(4+x)\le-5(2-x)$  a s v
e) $-5(6-5x)>-8(-3x-5)$  a s v
f) $-9(7-9x)\le4(20x-16)$  a s v


Question 9


Solve the following, showing your solution on a number line

a) $6(x+4)\ge4(x+9)$  a s v
b) $10(x+6)\ge15(x+4)$  a s v
c) $8(x-4)<14(x+5)$  a s v
d) $4(3x+2)>-3(4+x)$  a s v
e) $5(5-4x)<5(2x-1)$  a s v
f) $-5(2-x)\ge7(5+5x)$  a s v


Question 10


Solve the following, showing your solution on a number line

a) $2x+1> \frac{3x+75}{5}$  a s v
b) $3-2x> \frac{6+4x}{8}$  a s v
c) $4-6x\ge\frac{8x-1}{-5}$  a s v


Question 11


Solve the following, showing your solution on a number line

a) $5(x-8)+2(x-1)>0$  a s v
b) $4(x+5)+6(x+10)\le0$  a s v
c) $7(x-4)-(x+2)\ge0$  a s v
d) $3(2x+1)-4(x-3) < 16$  a s v
e) $0\le4(4x-1)-3(5x+4)$  a s v
f) $7(2x-3)\ge2(x+5)-4(6x-3)$  a s v


Question 12


Solve the following, showing your solution on a number line

a) $2x+4<3x<2x+9$  a s v
b) $7x-2\le8x\le7x+10$  a s v
c) $8x+8<10x\le8x+20$  a s v
d) $5x-9\le11x-3<5x+27$  a s v
e) $2(3x+5)\le7x\le3(2x+16)$  a s v
f) $9(8+4x)<40x+4\le12(3x+7)$  a s v


Question 13


By forming an inequation, solve the following

a) A bag contains only red balls or black balls. Out of a bag of $10$ balls. there are more red balls than black balls. How many red balls could there be?  a s v

b) A bag contains only green balls or yellow balls. Out of a bag of $50$ balls. there are more green balls than yellow balls. How many green balls could there be?  a s v