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Solving One-Step Equations
Choose Course
Algebra 1
One-Variable Equations
Solving One-Step Equations
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Solving One-Step Equations 1.3 - Solution
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Return to Solving One-Step Equations
a
To solve the equation, we need to isolate
x
x
x
on one side of the equation. Subtracting
2
2
2
from both sides will "cancel" it from the right-hand side.
6
=
x
+
2
6=x+2
6
=
x
+
2
SubEqn
LHS
−
2
=
RHS
−
2
\text{LHS}-2=\text{RHS}-2
LHS
−
2
=
RHS
−
2
6
−
2
=
x
+
2
−
2
6-2=x+2-2
6
−
2
=
x
+
2
−
2
SubTerms
Subtract terms
4
=
x
4=x
4
=
x
RearrangeEqn
Rearrange equation
x
=
4
x=4
x
=
4
b
To solve the equation we have to isolate
x
x
x
on one side. By adding
11
11
1
1
to both sides, we can cancel out
-
11
\text{-} 11
-
1
1
and isolate
q
.
q.
q
.
q
−
11
=
-
9
q-11=\text{-}9
q
−
1
1
=
-
9
AddEqn
LHS
+
11
=
RHS
+
11
\text{LHS}+11=\text{RHS}+11
LHS
+
1
1
=
RHS
+
1
1
q
−
11
+
11
=
-
9
+
11
q-11+11=\text{-}9+11
q
−
1
1
+
1
1
=
-
9
+
1
1
AddTerms
Add terms
q
=
2
q=2
q
=
2
c
To solve the equation we have to isolate
y
y
y
on one side of the equation. By dividing both sides of the equation by
-
7
,
\text{-}7,
-
7
,
we can remove the coefficient on the left-hand side.
-
7
y
=
28
\text{-}7y=28
-
7
y
=
2
8
DivEqn
LHS
/
(
-
7
)
=
RHS
/
(
-
7
)
\left.\text{LHS}\middle/(\text{-}7)\right.=\left.\text{RHS}\middle/(\text{-}7)\right.
LHS
/
(
-
7
)
=
RHS
/
(
-
7
)
-
7
y
-
7
=
28
-
7
\dfrac{\text{-}7y}{\text{-}7}=\dfrac{28}{\text{-}7}
-
7
-
7
y
=
-
7
2
8
SimpQuot
Simplify quotient
y
=
28
-
7
y=\dfrac{28}{\text{-}7}
y
=
-
7
2
8
MoveNegDenomToFrac
Put minus sign in front of fraction
y
=
-
28
7
y=\text{-}\dfrac{28}{7}
y
=
-
7
2
8
CalcQuot
Calculate quotient
y
=
-
4
y=\text{-}4
y
=
-
4
d
By multiplying both sides of the equation by
2
,
2,
2
,
we can eliminate the denominator and isolate
z
.
z.
z
.
14
=
z
2
14=\dfrac{z}{2}
1
4
=
2
z
MultEqn
LHS
⋅
2
=
RHS
⋅
2
\text{LHS} \cdot 2=\text{RHS}\cdot 2
LHS
⋅
2
=
RHS
⋅
2
14
⋅
2
=
z
2
⋅
2
14\cdot 2=\dfrac{z}{2}\cdot 2
1
4
⋅
2
=
2
z
⋅
2
FracMultDenomToNumber
a
2
⋅
2
=
a
\dfrac{a}{2}\cdot 2 = a
2
a
⋅
2
=
a
14
⋅
2
=
z
14\cdot 2=z
1
4
⋅
2
=
z
Multiply
Multiply
28
=
z
28=z
2
8
=
z
RearrangeEqn
Rearrange equation
z
=
28
z=28
z
=
2
8