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Which statement represents the simplified form of the given equation and correctly describes the solution?

12x-1=2(6+5x)+7

A.
x = 10; exactly one real solution
B.
19 = 19; infinite real solutions
C.
1 ≠ 19; no real solution
D.
x = 20; exactly one real solution

Sagot :

kaliaratliff
Let's solve your equation step-by-step.
12
x
−
1
=
2
(
6
+
5
x
)
+
7
Step 1: Simplify both sides of the equation.
12
x
−
1
=
2
(
6
+
5
x
)
+
7
12
x
+
−
1
=
(
2
)
(
6
)
+
(
2
)
(
5
x
)
+
7
(Distribute)
12
x
+
−
1
=
12
+
10
x
+
7
12
x
−
1
=
(
10
x
)
+
(
12
+
7
)
(Combine Like Terms)
12
x
−
1
=
10
x
+
19
12
x
−
1
=
10
x
+
19
Step 2: Subtract 10x from both sides.
12
x
−
1
−
10
x
=
10
x
+
19
−
10
x
2
x
−
1
=
19
Step 3: Add 1 to both sides.
2
x
−
1
+
1
=
19
+
1
2
x
=
20
Step 4: Divide both sides by 2.
2
x
2
=
20
2
x
=
10
A- X=10 exactly one solution
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