SME
Grade 7 Math · Problem type
px + q = r with negative numbers
Use this for “3x − 5 = 20” and “15 + 3x = 42”.
Diagram
3x − 5 = 16
3 × 7 − 5 = 21 − 5 = 16
This is an example. Type your own values to start a new problem.
p
x
+
(
q
)
=
r
x
One box
calculated
Formulas
p
×
x
+
q
=
r
(boxes
×
one
box
+
added
=
total)
3 × 7 + (−5) = 16
Assumptions
•
The bar is p equal boxes of x and a piece q, together as long as r.
•
A negative q is a piece taken off the end of the boxes.
•
Undo the adding first, then the multiplying.
Step-by-step
WE KNOW
p = 3 (boxes), q = −5 (added), r = 16 (total)
FIND
one box (x)
Step 1 · Find one box (x)
Use p × x + q = r (boxes × one box + added = total)
Take
q
from
both
sides,
then
divide
both
sides
by
p
.
Add
5
to
both
sides:
3
x
=
21
Divide
both
sides
by
3:
x
=
21
3
x
=
7
Check
Put the numbers back in. Both sides should match.
3 × 7 − 5 = 16 ✓
Topic check
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