SME
Grade 7 Math · Expressions & Equations
Two-step equations and inequalities
Use this for “Solve 3x + 2 = 11” with a balance of blocks and weights.
Diagram
Equation
Take away
Split
3x + 2 = 11
3 × 3 + 2 = 11
Level: both sides weigh 11.
This is an example. Type your own values to start a new problem.
p
x
+
q
=
r
x
Block weight
calculated
Formulas
p
×
x
+
q
=
r
(blocks
×
block
weight
+
weights
with
the
blocks
=
weights
on
the
right)
3 × 3 + 2 = 11
Assumptions
•
Every block weighs the same unknown amount x; every small weight weighs 1.
•
The hanger is level when both sides weigh the same: that is what = means.
•
Take the same from both sides, then share what is left among the blocks.
•
Check by putting x back in.
Step-by-step
WE KNOW
p = 3 (blocks), q = 2 (weights with the blocks), r = 11 (weights on the right)
FIND
block weight (x)
Step 1 · Find block weight (x)
Use p × x + q = r (blocks × block weight + weights with the blocks = weights on the right)
Take
q
from
both
sides,
then
divide
both
sides
by
p
.
Take
2
from
both
sides:
3
x
=
9
Divide
both
sides
by
3:
x
=
9
3
x
=
3
Check
Put the numbers back in. Both sides should match.
3 × 3 + 2 = 11 ✓
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