# Algebra - Solving Inequalities

a - answer    s - solution    v - video    d - discussion

## Question 1

Solve, showing your solution on a number line

a) $x-1>4$a s v d
b) $x-3<5$a s v d
c) $x-7>9$a s v d
d) $x-10\le20$a s v d
e) $x-50<2$a s v d
f) $x-78\ge13$a s v d

## Question 2

Solve, showing your solution on a number line

a) $x+2<7$a s v d
b) $x+5\ge11$a s v d
c) $x+10\le50$a s v d
d) $x+12>33$a s v d
e) $x+25\ge140$a s v d
f) $x+19>100$a s v d

## Question 3

Solve, showing your solution on a number line

a) $2x>10$a s v d
b) $6x>18$a s v d
c) $10x\le80$a s v d
d) $6x\ge36$a s v d
e) $7x<56$a s v d
f) $9x\le72$a s v d

## Question 4

Solve, showing your solution on a number line

a) $\frac x3\ge2$a s v d
b) $\frac x5\le5$a s v d
c) $\frac x9\le3$a s v d
d) $\frac x4>10$a s v d
e) $\frac {x}{11}<5$a s v d
f) $\frac {x}{12}\ge6$a s v d

## Question 5

Solve, showing your solution on a number line

a) $-2x<4$a s v d
b) $-5x>10$a s v d
c) $-3x\ge18$a s v d
d) $-8x\le64$a s v d
e) $-9x\ge99$a s v d
f) $-x<13$a s v d

## Question 6

Solve, showing your solution on a number line

a) $\frac {x}{-2}>3$a s v d
b) $-\frac {x}{4}\le5$a s v d
c) $\frac {x}{-6}\ge9$a s v d
d) $-\frac {x}{7}>11$a s v d
e) $-\frac {x}{3}<7$a s v d
f) $\frac {x}{-9}\le12$a s v d

## Question 7

Solve, showing your solution on a number line

a) $2x+3<13$a s v d
b) $4x-2\ge30$a s v d
c) $\frac x3+4\le10$a s v d
d) $\frac x7-3\le3$a s v d
e) $9x-13\ge5$a s v d
f) $\frac x9+17>25$a s v d

## Question 8

Solve, showing your solution on a number line

a) $12-2x>18$a s v d
b) $58-6x\ge100$a s v d
c) $\frac{x}{-5}+16\ge19$a s v d
d) $9-\frac{x}{2}\le15$a s v d
e) $90-10x<200$a s v d
f) $311-\frac x8<320$a s v d

## Question 9

Solve, showing your solution on a number line

a) $2(x+3)<14$a s v d
b) $3(x-2)\ge27$a s v d
c) $-5(x+3)\le-20$a s v d
d) $-7(x-5)>-63$a s v d
e) $6(x+5)<54$a s v d
f) $-20(x-1)\le-60$a s v d

## Question 10

Solve, showing your solution on a number line

a) $\frac{x+2}{5}>3$a s v d
b) $\frac{x-3}{6}>4$a s v d
c) $\frac{x+7}{2}\le8$a s v d
d) $-\frac{x+1}{7}>-10$a s v d
e) $\frac{x-3}{-8}\ge-6$a s v d
f) $-\frac{x-10}{9}\ge-11$a s v d

## Question 11

Solve, showing your solution on a number line

a) $4(8-x)<20$a s v d
b) $\frac{13-x}{6}\le2$a s v d
c) $7(10-x)\ge35$a s v d
d) $\frac{80-x}{8}\le8$a s v d
e) $-3(9-x)>-30$a s v d
f) $-\frac{17-x}{3}<4$a s v d

## Question 12

Solve, showing your solution on a number line

a) $4\le x+3\le5$a s v d
b) $7\le x-2\le10$a s v d
c) $10\le2x\le20$a s v d
d) $5\le\frac x2<8$a s v d
e) $19\le2x+3\le25$a s v d
f) $4\le5x-1<19$a s v d

## Question 13

Solve, showing your solution on a number line

a) $-10\le-2x\le-6$a s v d
b) $-7\le\frac{x}{-3}\le-5$a s v d
c) $-13\le3-2x\le1$a s v d
d) $3\le3-\frac{x}{5}\le8$a s v d
e) $-30\le-5(x-4)\le-10$a s v d
f) $-10\le\frac{5-5x}{6}<-5$a s v d

## Question 14

By forming an inequation, solve the following

a) I ate $5$ more chocolates than Harry. We lost count of how many chocolates we ate, but it was certainly more than $21$! What is the possible number of chocolates Harry ate?a s v d

b) Joe spent twice as much as Jenna on a shopping trip yesterday. They know they spent less than £$450$. How much could Jenna have spent?a s v d

c) The average of $3,6,7$ and $x$ is greater than or equal to $5$. What range of numbers could $x$ be?a s v d

d) The speed of a ball thrown down from a building is given as $s=3+9t$, where $s$ is the speed at which the ball is travelling in $m/s$ and $t$ is the time in seconds after the ball is thrown. At what times is the speed between $21m/s$ and $39m/s$?a s v d