Question

Solve the following equations using any method. Show your work and check your

Answer 1

a) The solution for the equation 2x + 16 = 5x + 4  is x=4.

b) The solution for the equation 3x − 5 = 2x + 14 is x=19.

c) The solution for the equation 5x − 5 = x + 15 is x=5.

Step-by-step explanation:

a) The given equation is  2x + 16 = 5x + 4

• From the above equation, it can be found that the equation consists of x terms and constant terms.
• Therefore, bring all the x terms on one side and the constant terms on other side of the equation.
• This gives the simplified form of the equation to solve for x value.

⇒ 16-4 = 5x-2x

⇒ 12 = 3x

⇒ x = 12/3

⇒ x = 4

The solution for the given equation is x=4.

To check, substitute x=4 in the equation :

2(4) + 16 = 5(4) + 4

8+16 = 20+4

24 = 24

Therefore, the solution x=4 satisfies the equation 2x + 16 = 5x + 4

Similarly,

b) The given equation is 3x − 5 = 2x + 14

⇒ 3x-2x = 14+5

⇒ x = 19

The solution for the given equation is x=19.

To check, substitute x=19 in the equation :

3(19) - 5 = 2(19) + 14

57-16 = 38+14

52 = 52

Therefore, the solution x=19 satisfies the equation 3x − 5 = 2x + 14

Similarly,

c) The given equation is 5x − 5 = x + 15

⇒ 5x-x = 15+5

⇒ 4x = 20

⇒ x = 20/4

⇒ x = 5

The solution for the given equation is x=5.

To check, substitute x=5 in the equation :

5(5) - 5 = 5 + 15

25-5 = 20

20 = 20

Therefore, the solution x=5 satisfies the equation 5x − 5 = x + 15