SME
Grade 8 Math · Problem type
Brackets first
Use this for “3(2x + 1) = 4x + 15”.
Chart
Left side: y = 6x + 3
Right side: y = 4x + 15
They cross at (6, 39).
6 × 6 + 3 = 39
4 × 6 + 15 = 39
This is an example. Type your own values to start a new problem.
p
(
a
x
+
b
)
=
c
x
+
d
A
Number of x after multiplying out
worked out (not typed)
B
Number after multiplying out
worked out (not typed)
x
x
worked out (not typed)
y
Value of each side
worked out (not typed)
Formulas
A
=
p
×
a
(number
of
x
after
multiplying
out
=
number
outside
×
x
in
the
brackets)
6 = 3 × 2
B
=
p
×
b
(number
after
multiplying
out
=
number
outside
×
number
in
the
brackets)
3 = 3 × 1
A
×
x
+
B
=
c
×
x
+
d
(number
of
x
after
multiplying
out
×
x
+
number
after
multiplying
out
=
x
on
the
right
×
x
+
number
on
the
right)
6 × 6 + 3 = 4 × 6 + 15
y
=
c
×
x
+
d
(value
of
each
side
=
x
on
the
right
×
x
+
number
on
the
right)
39 = 4 × 6 + 15
Assumptions
•
Multiply everything inside the brackets by the number outside: p(ax + b) = pax + pb.
•
Then solve Ax + B = cx + d as on the balance.
•
On a graph, each side is a line; the solution is the x where they cross.
Step-by-step
WE KNOW
p = 3 (number outside), a = 2 (x in the brackets), b = 1 (number in the brackets), c = 4 (x on the right), d = 15 (number on the right)
FIND
number of x after multiplying out (A), number after multiplying out (B), x (x), value of each side (y)
Step 1 · Find number of x after multiplying out (A)
Use A = p × a (number of x after multiplying out = number outside × x in the brackets)
Multiply
the
x
in
the
brackets
by
the
number
outside.
A
=
3
×
2
A
=
6
Step 2 · Find number after multiplying out (B)
Use B = p × b (number after multiplying out = number outside × number in the brackets)
Multiply the number in the brackets too: every term inside.
B
=
3
×
1
B
=
3
Step 3 · Find x (x)
Use A × x + B = c × x + d (number of x after multiplying out × x + number after multiplying out = 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.
Take
4
x
from
both
sides:
2
x
+
3
=
15
Take
3
from
both
sides:
2
x
=
12
Divide
both
sides
by
2:
x
=
6
x
=
6
Step 4 · Find value of each side (y)
Use y = c × x + d (value of each side = x on the right × x + number on the right)
Check: both sides come to this.
y
=
4
×
6
+
15
Left side: 3 × (2 × 6 + 1) = 3 × 13 = 39
y
=
39
Check
Put the numbers back in. Both sides should match.
6 = 3 × 2 ✓
3 = 3 × 1 ✓
6 × 6 + 3 = 4 × 6 + 15 ✓
39 = 4 × 6 + 15 ✓
Topic check
See what you know: 5 questions on this topic
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