SOLVING TWO STEP EQUATIONS

Solve each of the following equation.

Example 1 :

4x+5 = 29

Solution :

4x+5 = 29

Subtract 5 on both sides, we get

4x = 29-5

4x= 24

Divide by 4 on both sides, we get

x = 24/4

x = 6

Example 2 :

7-5x = 22

Solution :

7-5x = 22

Subtract 7 on both sides, we get

-5x = 22-7

-5x = 15

Divide by -5 on both sides, we get

x = 15/(-5)

x = -3

Example 3 :

(x/6) - 12 = 8

Solution :

(x/6) - 12 = 8

Add 12 on both sides.

x/6 = 8 + 12

x/2 = 20

Multiply by 2 on both sides.

x = 20(2)

x = 40

Example 4 :

Which of the following equations equivalent to 2x + 13 = -5 ?

(a) 2x+5 = -13  (b) x = 2(-5-13) 

(c) x+13 = -2.5  (d) 2x+11 = -3

Solution :

By observing the options, in option (a)

we have 5 in the left side. To get that we can add 5 on both sides.

2x + 13 = -5 

Add 5 on both sides and subtract 13 on both sides.

2x+5 = -13

So, option (a) is correct.

Example 5 :

(2x/5) - 7 = 3

Solution :

(2x/5) - 7 = 3

Add 7 on both sides

2x/5 = 3+7

2x/5 = 10

Multiply by 5 on both sides

2x = 10(5)

2x = 50

Divide by 2 on both sides.

x = 50/2

x = 25.

Example 6 :

A number g is decreased by 23 and then multiplied by 1/2. The result is 8 more than twice the number g.

Solution :

(1/2)(g - 23) = 2g + 8

Multiply by 2 on both sides, we get

g-23 = 2(2g+8)

g - 23 = 4g +16

Subtract 4g on both sides, we get

g-4g-23 = 16

-3g - 23 = 16

Add 23 on both sides.

-3g = 16+23

-3g = 39

Divide by -3 on both sides.

g = 39/(-3)

g = -13

Example 7 :

Nine less than twice x is three more than x. What is the value of x?

Solution :

2x - 9 = x+3

Subtract x on both sides

2x - x - 9 = 3

x - 9 = 3

Add 9 on both sides, we get

x = 3+9

x = 12

Example 8 :

Eight less than four times the number c is twenty. What is the value of c?

Solution :

4c - 8 = 20

Add 8 on both sides, we get

4x = 20 + 8

4x = 28

Divide by 4 on both sides, we get

x = 28/4

x = 7

Example 9 :

The sum of four consecutive odd integers is 296. What is the greatest of the four consecutive odd integers?

Solution :

Let x be the first odd number. Its consecutive number = x + 2

First four consecutive odd numbers are x, x + 2, x + 4, x + 6.

x+x+2+x+4+x+6 = 296

4x+12 = 296

Subtract 12 on both sides, we get

4x = 296-12

4x = 284

Divide by 4 on both sides, we get

x = 284/4

x = 71

.The greatest number = x + 6

= 71+ 6

= 77

So, 77 is the greatest odd number.

Example 10 :

The sum of four consecutive integers is -54.

Solution :

Let x be the first number.

Four consecutive numbers be x, x+1, x+2, x+3.

x+x+1+x+2+x+3 = -54

4x+6 = -54

Subtract 6 on both sides.

4x = -54-6

4x = -60

Divide by 4 on both sides, we get

x = -60/4

x = -15

Example 11 :

Describe and correct the error in solving the equation.

Solution :

28y + 7 = 21

Subtracting 7 on both sides

28y = 21 - 7

28y = 14

Dividing by 28 on both sides

y = 14/28

y = 1/2

The error is, instead of subtracting 7 on both sides, it is been added.

Example 12 :

You go on a hike with your uncle. Your backpack weighs 25 pounds. Your uncle is a math teacher and he tells you that your pack is 7 pounds less than twice as heavy as his pack. Use the equation 2p − 7 = 25 to find the weight of your uncle’s backpack.

Solution :

2p − 7 = 25

Adding 7 on both sides, we get

2p = 25 + 7

2p = 32

Dividing by 2, we get

p = 32/2

p = 16

Example 13 :

You pilot a helicopter tour from Orlando to West Palm Beach along the coast. On the return trip, you fly straight back to Orlando at a steady speed in 1.3 hours. The total distance is 313 miles. Write and solve an equation to find your speed from West Palm Beach to Orlando.

Solution :

Total distance traveled = 313 miles.

Time taken = 1.3 hours

Time = distance / speed

1.3 = 313 / speed

Speed = 313/1.3

= 240.76

So, the speed is 240.76 miles per hour.