4 Linear relationships
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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