Solve each equation

Question

Solve. 

A. -2.6 + x = 8.3

B. 4 1/2 + y = 8 1/3 

C. -3/4x = 36

 

Answer 1

A) The equation is -2.6 + x = 8.3.

Add 2.6 to each side.

2.6 - 2.6 + x = 2.6 + 8.3

0 + x = 2.6 + 8.3

Apply Identity Property or Zero Property of Addition: 0 + a = a.

x = 2.6 + 8.3

x = 10.9.

The solution is x = 10.9.

B) The equation is 4 1/2 + y = 8 1/3.

Convert the mixed fraction into fraction.

9/2 + y = 25/3

Subtract each side by 9/2.

9/2 + y - 9/2 = 25/3 - 9/2

Apply Commutative property of addition: a + b = b + a.

y + 9/2 - 9/2 = 25/3 - 9/2

y + 0 = 25/3 - 9/2

Apply Identity Property or Zero Property of Addition: 0 + a = a.

y = 25/3 - 9/2

Take LCM of 2 and 3 i.e, 6.

y = (50 - 27)/6

y = 23/6.

The solution is y = 23/6.

C) The given equation -3/4x = 36 can be read as (-3/4) x = 36 or -3/(4x) = 36

Solve first equation -3/4 x = 36.

-3x / 4 = 36

Multiply by 4 to each side.

(-3x / 4)*4 = 36 *4

-3x = 144

-3x/-3 = 144/-3

x = -144/3

x = -48.

The solution is x = -48.

Solve second equation -3 / (4x) = 36.

Multiply each side by 4x.

(-3 / 4x)4x = (36)4x

-3 = 36(4x)

-3 = 144x

Divide each side by 144.

-3 / 144 = 144x / 144

x = -3 / 144

x = -1/48.

The solution is x = -1/48.