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in Algebra by (65.5k points)

Solve the Mowing equations :

(a) 2(x+4) = 12

(b) 3(n – 5) = 21

(c) 3 (n – 5) = -21

(d) -4(2 + x) = 8

(e) 4 (2 – x) = 8

1 Answer

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Best answer

(a) 2(x+4) = 12

The given equation is 2(x + 4) = 12
Divide by 2 both the sides

x + 4 = 6
Transpose +4 from LHS to RHS x = 6 – 4 (on transposing 4 becomes -4)
∴ x = 2
Substitute the value of x = 2 in the given equation
2(x + 4) = 12
2(2 + 4) = 12
2(6) = 12
12 = 12
∴ LHS = RHS (verified)

(b) 3(n – 5) = 21

The given equation is 3 (n – 5) = 21
Divide by 3 both the sides

∴ n – 5 = 7
Transpose -5 from LHS to RHS
n = 7 + 5 [on transposing -5 becomes +5]
∴ n = 12
Substitute the value of n = 12 in the given equation
3(n – 5) = 21
3(12 – 5) = 21
3(7) = 21
21 = 21
LHS = RHS (verified)

(c) 3 (n – 5) = -21

The given equation is 3 (n – 5) = -21
Divide by 3 both the sides 3

Transpose -5 from LHS to RHS n = -7 + 5 (on transposing -5 becomes +5)
n = -2
Substitute the value n = -2 in the given equation
3 (n – 5) = -21 .
3(-2 – 5) = -21
3(-7) = -21
-21 = -21
∴ LHS = RHS (verified)

(d) -4(2 + x) = 8

The given equation is -4 (2 + x) = 8
Divide by -4 both the sides

2 + x = -2
Transpose 2 from LHS to RHS x = -2 -2 [on transposing 2 becomes -2]
∴ x = -4
Substitute the value of x = -4 in the given equation
-4(2 + x) = 8
-4(2 – 4) = 8
-4 (-2) = 8
8 = 8
∴ LHS = RHS (verified)

(e) 4 (2 – x) = 8

The given equation is 4 (2 – x) = 8
Divide by 4 both the sides

2 – x = 2
Transpose +2 from LHS to RHS
-x = 2 – 2 (on transposing 2 becomes -2)
-x = 0
multiply by -1 both the sides
-x × -1 = 0 × -1 x = 0
Substituting the value of x = 0 in the given equation
4(2 – x) = 8
4(2 – 0) = 8
8 – 0 = 8
8 = 8
∴ LHS = RHS (verified)

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