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

Answer 2

B) The equation is 4 1/2 + y = 8 1/3.

Convert the mixed fraction into improper fraction. a b/c = a + b/c = ((a * c) + b) / c

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

Fractions with different denominators can not be subtracted. So, write the equation with common denominator.

Find the least common denominator L.C.M.

Multiples of 2 = 2, 4, 6, 8

Multiples of 3 = 3, 6, 9, 12

Least Common Multiple of 2 and 3 is 6

Write the right hand side equation with common denominator

y = (25 * 2)/ (3 * 2) - (9 * 3) / (2 * 3)

y = 50/6 - 27 / 6.

Since denominators are same subtract the numerators over the denominator

y = (50 - 27)/6

y = 23/6

Write the improper fraction as mixed number

y = 18/6 + 5 /6

y = 3 5/6

 

Answer 3

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.