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? ? 5 × 2 ? ? 8 − 5 ? ? 3 ; 2 ? ? 5 × 6 ? ? 9 ÷ 2 ? ? 7 ; 5
x 2 × x 2 × x 1 7 6 3 × 2 ÷ 2 − 1 x 17 4 x 3 3 x 5 5 x 1 2 x 10 8 x 2 4 x 14 3 x 2 x 6 7 × x 4 2 × x 14 − 4 − 4 7 × x 2 × x 10 − 2 × x − 2 × x 5 × x 10 ÷ 5 ÷ 5 x 2
1.
Reverse
op er ations
E.11562
On
eac h
of
the
diagrams
b elo w,
com- plete
the
missing
information
:
1
Complete
the
follo wing
diagrams
:
2
Giv e
the
solutions
to
eac h
of
the
follo wing
equations
:
a
x
+
3
=
5
b
2
×
x
=
8
c
x
−
5
=
3
d
x
+
3.2
=
5
e
6
×
x
=
9
f
x
÷
2
=
7.5
E.11569
L’exercice
n’existe
pas.
2.
ˇOne-sidedı
e quations
E.11563
Note:
For
equation
(2
×
x
)+1= 7
,
finding
solutions
is
easy
b ecause,
using
the
order
of
op erations,
y ou
simply
need
to
see
ho w
the
expression
on
the
left
side
is
constructed
to
ob- tain
the
n umerical
v alue
on
the
righ t
side.
The
diagram
b elo w
sho ws
this
solution
:
The
solution
to
equation
2
×
x
+1= 7
is
the
n um b er
3
.
Determine
the
solution
to
equation
7
×
x
+3= 17
by
complet- ing
the
diagram
b elo w
:
3.
Two-sided
e quations
E.11564
Determine,
for
eac h
question,
the
v alue
of
x
achieving
equilibrium
of
the
balance
:
a
b
c
d
E.11565
Method
:
To
solv e
the
equation
:
7
×
x
+
4
=
2
×
x
+
14
We
transform
it
step
b y
step
to
arriv e
at
the
final
step
in
the
form
ˇ
x
=
:
:
:
‘’,
whic h
allo ws
us
to
obtain
the
solution
to
this
equation.
Here
is
a
suggested
transformation
in
sev eral
steps
to
obtain
the
solution
to
the
equation
:
Solve
the
follo wing
equations
:
a
5
×
x
+
7
=
3
×
x
+
13
b
2
×
x
+
1
=
x
+
8
c
9
×
x
+
6
=
5
×
x
+
14
d
4
×
x
+
1
=
x
+
10
4.
System
of
e quations :
intr o duction
to
substitution
https:/ /c hingmath.fr
chapExoCorrec/11562 sacados/11562 ? ? 5 × 2 ? ? 8 − 5 ? ? 3 ; 2 ? ? 5 × 6 ? ? 9 ÷ 2 ? ? 7 ; 5 sacados/11569 chapExoCorrec/11563 sacados/11563 x 2 × x 2 × x 1 7 6 3 × 2 ÷ 2 − 1 x 17 chapExoCorrec/11564 sacados/11564 4 x 3 3 x 5 5 x 1 2 x 10 8 x 2 4 x 14 3 x 2 x 6 chapExoCorrec/11565 sacados/11565 7 × x 4 2 × x 14 − 4 − 4 7 × x 2 × x 10 − 2 × x − 2 × x 5 × x 10 ÷ 5 ÷ 5 x 2
E.11566
W e
kno w
the
follo wing
relationships
:
We
ha v e
the
v alue
:
=.
.
.
https:/ /c hingmath.fr
sacados/11566