SME
Grade 6 Math · Problem type
Solutions of inequalities
Use this for “Is 23 a solution of 2n < 47?” or “Which numbers make p > 8 true?”
Diagram
n <
n ≤
n >
n ≥
n < 23.5: every number less than 23.5.
The open circle leaves out 23.5.
Test 23: 23 < 23.5 is true.
This is an example. Type your own values to start a new problem.
n
n
Value of n to test
example
p
Left side at the test value
worked out (not typed)
e
Boundary
worked out (not typed)
h
A solution?
worked out (not typed)
Formulas
a
×
n
=
p
(coefficient
×
value
of
n
to
test
=
left
side
at
the
test
value)
2 × 23 = 46
c
÷
a
=
e
(bound
÷
coefficient
=
boundary)
47 ÷ 2 = 23.5
Is
p
s
c
true?
h
(left
side
compared
with
the
bound
=
a
solution?)
Is 46 < 47 true? yes
Assumptions
•
A solution makes the inequality true. Put the value in and compare the two sides.
•
The boundary is where the two sides are equal: 2n = 47 at n = 23.5.
•
< and > leave the boundary out (open circle); ≤ and ≥ take it in (closed circle).
•
Tap the sign in the inequality to change it: <, ≤, > or ≥.
•
Coefficients from 0.01 to 100; bounds and values from −1,000 to 1,000.
Step-by-step
WE KNOW
a = 2 (coefficient), c = 47 (bound), n = 23 (value of n to test), s: <
FIND
left side at the test value (p), boundary (e), a solution? (h)
Step 1 · Find left side at the test value (p)
Use a × n = p (coefficient × value of n to test = left side at the test value)
Put the value in: work out the left side.
p
=
2
×
23
p
=
46
Step 2 · Find boundary (e)
Use c ÷ a = e (bound ÷ coefficient = boundary)
The boundary: the value that makes the two sides equal.
e
=
47
2
2
3
.
5
2
)
4
7
.
0
−
4
7
−
6
1
0
−
1
0
0
e
=
23.5
(the
greatest
whole-number
solution
is
23)
Step 3 · Find a solution? (h)
Use Is p s c true? h (left side compared with the bound = a solution?)
Is the inequality true with the value put in? Then the value is a solution.
46
<
47:
h
46 < 47 is true
h
=
yes
Check
Put the numbers back in. Both sides should match.
2 × 23 = 46 ✓
47 ÷ 2 = 23.5 ✓
46 < 47 ✓
Topic check
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