3 Linear equations

Worksheet

1

State the inequality for x that is represented on the following number lines:

a

b

c

d

e

f

g

h

2

Plot the following inequalities on a number line:

a

x \lt 0

b

x \geq 6

c

x \leq 1

d

x \geq 0.6

e

x \geq 0

f

x \leq 2

g

x > 1

h

x < - \dfrac{3}{4}

3

Jenny tried to solve the following inequality but made a mistake in her work:

\begin{alignedat}{4} \text{Step 0:} & -27 & -9 & x & & < & 36 \\ \text{Step 1:} & & -9 & x & & < & 63 \\ \text{Step 2:} & & & x & & < & -7 \end{alignedat}

Determine which step is incorrect and explain the error.

4

Consider the following inequalities:

i

Solve the inequality.

ii

Plot the inequality on a number line.

a

7 x \leq 63

b

- 4 x \leq 20

c

15 \gt - 3 x

d

x - 1 \lt 4

e

1 + x \leq 1

f

- 5 + x \leq 1

g

6 - x \gt 10

h

2 x - 8 \lt 4

i

- 3 x + 7 \geq 4

j

10 - 8 x \lt 26

k

2 \left(x + 5\right) \gt 4

l

4 \left( 2 x + 4\right) \gt 40

m

3 \left( 4 x + 8\right) \leq - 12

n

\dfrac{x}{5} \gt \dfrac{8}{5}

o

\dfrac{x}{6} \geq 2

p

\dfrac{x}{3} - 1 \leq - 5

q

2 - \dfrac{x}{4} \geq 0

r

\dfrac{x - 6}{3} \leq - 2

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Solve linear inequalities and graph their solutions on a number line.