**Simple Equations**

**Question 1.****Complete the last column of the table.**

**Solution:**

**Question 2.****Check whether the value given in the brackets is a solution to the given equation or not :(a)** n + 5 = 19 (n = 1)

**(b)**7n + 5 = 19 (w = -2)

**(c)**7n + 5 = 19 (n = 2)

**(d)**4p – 3 = 13(p = 1)

**(e)**4p-3 = 13(p = -4)

**(f)**4p – 3 = 13 (p = 0)

**Solution:**

**Question 3.****Solve the following equations by trial and error method :(i)** 5p + 2 = 17 .

**(ii)**3m – 14 = 4

**Solution:****(i)** Let us evaluate the L.H.S. and R.H.S. of the given equation for some values of p and continue to given new values till the L.H.S. becomes equal to the R.H.S.

The given equation is 5p + 2 = 17. We have,

L.H.S. = 5p+ 2 and R.H.S. = 17

Clearly, L.H.S. = R.H.S. for p = 3. Hence, p = 3 is the solution of the given equation.

**(ii)** Let us evaluate the L.H.S. and R.H.S. of the given equation for some values of m and continue to given new values till the L.H.S. becomes equal to the R.H.S.

The given equation is 3m – 14 = 4, that is, 14 subtracted from 3 times m gives 4. So, we substitute values which gives 3m > 14. We have, L.H.S. = 3m – 14 and R.H.S. = 4

Clearly, L.H.S. = R.H.S. for m = 6. Hence, m = 6 is the solution of the given equation.

**Question 4.****Write equations for the following statements :**

- The sum of numbers x and 4 is 9.
- 2 subtracted from y is 8.
- Ten times a is 70.
- The number b divided by 5 gives 6.
- Three-fourth of t is 15.
- Seven times m plus 7 gets you 77.
- One fourth of a number x minus 4 gives 4.
- If you take away 6 from 6 times y, you get 60.
- If you add 3 to one third of z, you get 30.

**Solution:**

The equations for the given statements are :

- x + 4 = 9
- y – 2 = 8
- 10 a = 70
- b ÷ 5 = 6
- × t = 15
- 7m + 7 = 77
- × x – 4 = 4
- 6y – 6 = 60
- × z + 3 = 30

**Question 5.****Write the following equations in statement forms :**

- p + 4 = 15
- m – 7 = 3
- 2m = 7
- = 3
- = 6
- 3p + 4 = 25
- 4p – 2 = 18
- + 2 = 8

**Solution:**The statements for the given equations are :

- The sum of numbers p and 4 is 15.
- The difference of m and 7 is 3.
- Two times m is 7.
- The number m divided by 5 gives 3.
- Three time’s m divided by 5 gives 6.
- Three times p plus 4 gives 25.
- Four times p minus 2 gives 18.
- p divided by 2 plus 2 gives 8.

**Question 6.****Set up an equation in the following cases :(i)** Irfan says that he has 7 marbles more than five times the marbles Parxnit has. Irfan has 37 marbles. (Take m to be the number of Permits marbles.)

**(ii)** Laxmi’s father is 49 years old. He is 4 years older than three times Laxmi’s age. (Take Laxmi’s age to be y years.)

**(iii)** The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. (Take the lowest score to be l.)

**(iv)** In an isosceles triangle, the vertex angle is twice either base angle. (Let the base angle be b in degrees. Remember that the sum of angles of a triangle is 180 degrees).

**Solution:****(i)** Let the number of marbles with Parmit be m.

Then, 7 added to 5 times mis 5m + 7

It is given that 7 marbles more than five times the marble is 37. Thus, the equation obtained is 5m + 7 = 37.

**(ii)** Let Laxmi’s age be y years. Then, 4 added to 3 times y is 3y + 4

It is given that the father is 4 years older than 3 times Laxmi’s age. His age is 49years.

Then, we have the following equation : 3y + 4 = 49

**(iii)** Let the lowest marks be l. Then, twice the lowest marks plus 7 is 2l +7

It is given that, the highest marks 87 obtained by a student is twice the lowest marks plus 7.

So, we have the following equation : 2l + 7 = 87

**(iv)** Let the base angle be b. Then, the vertex angle = 2b.

Since, sum of the angles of a triangle is 180°

∴ b + b + 2b = 180°

⇒ 4b = 180°

which is the required.equation.