SOLVING ONE STEP EQUATIONS WITH DECIMALS

In the following exercises, solve the equation.

Problem 1 :

y + 2.9 = 5.7

Solution :

The inverse operation of addition is subtraction. So, subtract 2.9 from both sides.

y + 2.9 – 2.9 = 5.7 – 2.9

Simplify,

y = 2.8

Problem 2 :

m + 4.6 = 6.5

Solution :

The inverse operation of addition is subtraction. So, subtract 4.6 from both sides.

m + 4.6 – 4.6 = 6.5 – 4.6

By subtracting, we get

m = 1.9

Problem 3 :

h + 4.37 = 3.5

Solution :

The inverse operation of addition is subtraction. So, subtract 4.37 from both sides.

h + 4.37 – 4.37 = 3.5 – 4.37

By subtracting, we get

h = - 0.87

Problem 4 :

a + 6.2 = - 1.7

Solution :

The inverse operation of addition is subtraction. So, subtract 6.2 from both sides.

a + 6.2 – 6.2 = - 1.7 – 6.2

By adding, we get

a = - 7.9

Problem 5 :

-2.7 u = -9.72

Solution :

The inverse operation of multiplication is division. So, divide both sides by -2.7.

-2.7 u / -2.7 = -9.72 / -2.7

By dividing, we get

u = 3.6

Problem 6 :

a / 0.4 = - 20

Solution :

To isolate the variable a (to get a coefficient of 1), multiply both sides by 0.4.

(a / 0.4) (0.4) = (-20) (0.4)

By multiplying, we get

a = - 8

Problem 7 :

x / 0.7 = - 0.4

Solution :

To isolate the variable x (to get a coefficient of 1), multiply both sides by 0.7.

(x / 0.7) (0.7) = (- 0.4) (0.7)

By multiplying, we get

x = - 0.28

Problem 8 :

y / 0.8 = - 0.7

Solution :

To isolate the variable y (to get a coefficient of 1), multiply both sides by 0.8.

(y / 0.8) (0.8) = (- 0.7) (0.8)

By multiplying, we get

y = - 0.56

Problem 9 :

q - 0.47 = - 1.53

Solution :

The inverse operation of subtraction is addition. So, add 0.47 from both sides.

q – 0.47 + 0.47 = - 1.53 + 0.47

By subtracting, we get

q = - 1.06

Problem 10 :

0.5 x = 3.5

Solution :

The inverse operation of multiplication is division. So, divide both sides by -0.5.

0.5 x / 0.5 = 3.5 / 0.5

By dividing, we get

x = 7

Problem 11 :

-1.7 c = 8.5

Solution :

The inverse operation of multiplication is division. So, divide both sides by -1.7.

-1.7 c / -1.7 = 8.5 / -1.7

By dividing, we get

c = - 5

Problem 12 :

-2.9 x = 5.8

Solution :

The inverse operation of multiplication is division. So, divide both sides by -2.9.

-2.9 x / -2.9 = 5.8 / -2.9

By dividing, we get

x = - 2

Problem 13 :

Describe and correct the error in solving the equation.

Solution :

Given equation is -1.5 + k = 8.2

Descrining the error :

In the given work, since we have -1.5 in order ot remove it, we have to add 1.5 on both sides.

Solving it correctly :

k = 8.2 + 1.5

k = 9.7

So, the correct value of k is 9.7

Problem 14 :

A gym teacher orders 42 tennis balls. Each package contains 3 tennis balls. Which of the following equations represents the number x of packages?

a)  x + 3 = 42     b)  3x = 42       c)  x/3 = 42      d)  x = 3/42

Solution :

Number of tennis balls = 42

Number of balls in each package = 3

Let x be the number of packages.

Number of packages · number of balls in each package = 42

x · 3 = 42

3x = 42

So, option b is correct.

Problem 15 :

You clean a community park for 6.5 hours. You earn $42.25. How much do you earn per hour?

Solution :

Let x be the amount you are earning per hour.

Number of hours working = 6.5 hours

Total amount you earn = $42.25

Number of hours working · earninign per hour = 42.25

6.5 · x = 42.25

x = 42.25/6.5

x = 6.5

So, the amount you are earning per hour is $6.5

Problem 16 :

A rocket is scheduled to launch from a command center in 3.75 hours. What time is it now?

Solution :

Let x be the required time.

3 hours and 0.75 hours To convert 0.75 hours into minutes, we use the following conversion.

1 hour = 60 minutes

0.75 hours = 0.75 x 60

= 45 minutes

So, 3.75 hours is 3 hours and 45 minutes.

To get the time now, we have to subtract 3 : 45 hours from 11 : 20 hours.

= 11 : 20 - 3 : 45

= 10 : 80 - 3 : 45

= 7 : 35

So, the time now is 7 : 35 am

Problem 17 :

After earning interest, the balance of an account is $420. The new balance is 7/6 of the original balance. How much interest did it earn?

Solution :

Balance of an account = $420

New balance = 7/6 of original balance

= 7/6 of 420

= (7/6) x 420

= 7 x 70

= 490

So, the intrest is $490.