SME
Grade 8 Math · Expressions & Equations
Linear equations with variables on both sides
Use this for “Solve 3x + 4 = x + 10” with variables on both sides.
Diagram
3x + 4 = x + 10
On the left: 3 × 3 + 4 = 13
On the right: 1 × 3 + 10 = 13
Level when x = 3: both sides weigh the same.
Take x and 4 from both sides: 2x = 6
This is an example. Type your own values to start a new problem.
a
x
+
b
=
c
x
+
d
x
Weight of one x-block
worked out (not typed)
Formulas
a
×
x
+
b
=
c
×
x
+
d
(x-blocks
on
the
left
×
weight
of
one
x-block
+
counters
on
the
left
=
x-blocks
on
the
right
×
weight
of
one
x-block
+
counters
on
the
right)
3 × 3 + 4 = 1 × 3 + 10
Assumptions
•
Each x-block weighs the same unknown amount x; each counter weighs 1.
•
Taking the same weight from both pans keeps the balance level.
•
Gather the x-blocks on one side and the counters on the other, then divide.
•
Check by putting x back into both sides.
Step-by-step
WE KNOW
a = 3 (x-blocks on the left), b = 4 (counters on the left), c = 1 (x-blocks on the right), d = 10 (counters on the right)
FIND
weight of one x-block (x)
Step 1 · Find weight of one x-block (x)
Use a × x + b = c × x + d (x-blocks on the left × weight of one x-block + counters on the left = x-blocks on the right × weight of one x-block + counters on the right)
Take
the
same
x
and
the
same
number
from
both
sides,
then
divide
by
the
x
left.
3?
+
4
=
x
+
10
Take
x
from
both
sides:
2
x
+
4
=
10
Take
4
from
both
sides:
2
x
=
6
Divide
both
sides
by
2:
x
=
3
x
=
3
Check
Put the numbers back in. Both sides should match.
3 × 3 + 4 = 1 × 3 + 10 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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Use this for “What do you do first to solve 3x + 4 = x + 10?”