SME
Grade 8 Math · Problem type
Negatives on a balance
Use this for “4x − 7 = −2x + 11” or “2x − 3 = −x + 6”.
Diagram
2x − 3 = −x + 6
On the left: 2 × 3 − 3 = 3
On the right: −1 × 3 + 6 = 3
Level when x = 3: both sides weigh the same.
This is an example. Type your own values to start a new problem.
a
x
+
(
b
)
=
c
x
+
d
x
x
worked out (not typed)
Formulas
a
×
x
+
b
=
c
×
x
+
d
(x
on
the
left
×
x
+
number
on
the
left
=
x
on
the
right
×
x
+
number
on
the
right)
2 × 3 + (−3) = −1 × 3 + 6
Assumptions
•
A balloon pulls its pan up: a balloon marked −x takes away one x, one marked −1 takes away 1.
•
Adding the same to both sides keeps the balance level: add 3 to cancel a −3.
•
The balance is level when both sides come to the same amount.
Step-by-step
WE KNOW
a = 2 (x on the left), b = −3 (number on the left), c = −1 (x on the right), d = 6 (number on the right)
FIND
x (x)
Step 1 · Find x (x)
Use a × x + b = c × x + d (x on the left × x + number on the left = x on the right × x + number on the right)
Take
the
same
x
and
the
same
number
from
both
sides,
then
divide
by
the
x
left.
2?
−
3
=
−
x
+
6
Add
x
to
both
sides:
3
x
−
3
=
6
Add
3
to
both
sides:
3
x
=
9
Divide
both
sides
by
3:
x
=
3
x
=
3
Check
Put the numbers back in. Both sides should match.
2 × 3 + (−3) = −1 × 3 + 6 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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