SME
Grade 9 Math · Algebra 1
Solving linear equations and literal equations (rearranging formulas)
Use this for “Solve 5x + 1 = 2x + 10” and other linear equations with x on both sides.
Diagram
5x + 1 = 2x + 10.
x = 3: each side is 16.
This is an example. Type your own values to start a new problem.
a
x
+
b
=
c
x
+
d
x
=
Formulas
a
×
x
+
b
=
c
×
x
+
d
5 × 3 + 1 = 2 × 3 + 10
Assumptions
•
Doing the same thing to both sides keeps the equation true.
•
Collect the x terms on the side with the larger coefficient, so the x term stays positive.
•
When a = c there is no solution (b ≠ d) or every number is a solution (b = d).
Step-by-step
WE KNOW
d = 10, a = 5, b = 1, c = 2
FIND
solution (x)
Step 1 · Find solution (x)
Use a × x + b = c × x + d
Take
cx
from
both
sides
so
the
x
terms
are
on
the
left,
take
b
away,
then
divide.
x
=
d
−
b
a
−
c
x
=
10 − 1
5 − 2
Take
2
x
from
both
sides:
3
x
+
1
=
10
Take
1
from
both
sides:
3
x
=
9
Divide
both
sides
by
3:
x
=
3
x
=
3
Check
Put the numbers back in. Both sides should match.
5 × 3 + 1 = 2 × 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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