Math virtual assistant

Calculators Topics Go Premium About Snapxam
ENGESP
Topics

Step-by-step Solution

Solve the inequality $2\left(x+1\right)-3\left(x-2\right)\leq x+6$

Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Answer

$x\geq 1$

Step-by-step explanation

Problem to solve:

$2\left(x+1\right)-3\left(x-2\right)\leq x+6$
1

Grouping terms

$2\left(x+1\right)-3\left(x-2\right)-x\leq 6$
2

Solve the product $2\left(x+1\right)$

$2x+2-3\left(x-2\right)-x\leq 6$
3

Adding $2x$ and $-1x$

$x+2-3\left(x-2\right)\leq 6$
4

Solve the product $-3\left(x-2\right)$

$8+x-3x\leq 6$
5

Adding $-3x$ and $x$

$-2x+8\leq 6$
6

Moving the term $8$ to the other side of the inequation with opposite sign

$-2x\leq -2$
7

Multiply both sides of the inequality by $-1$, reversing the sign

$2x\geq 2$
8

Divide both sides of the inequation by $2$

$x\geq 1$

Answer

$x\geq 1$

Problem Analysis

$2\left(x+1\right)-3\left(x-2\right)\leq x+6$

Main topic:

Inequalities

Time to solve it:

~ 1.59 seconds