Question

State which of the following are equations with a variable. In case of an equation with a variable, Identify the variable.

(1). 17 + x = 5

(2). 2b - 3 = 7

(3). (y - 7) > 5

(4). 9/3 = 3

(5). 7 × 3 - 19 = 2​

Answer 1

Question :

State which of the following are equations with a variable. In case of an equation with a variable, Identify the variable.

(1). 17 + x = 5

(2). 2b - 3 = 7

(3). (y - 7) > 5

(4). 9/3 = 3

(5). 7 × 3 - 19 = 2​

$\rule{200}{1}$

Concept :

Equation with a variable : An equation which has '=' sign and has a variable i.e. x , y, z, a, b, c etc. in the LHS or RHS part of '=' is an equation with a variable.

Solution :

1) 17 + x = 5

$\longmapsto$ This equation has '=' sign and a variable 'x'.

∴ It's an equation with a variable 'x'

$\rule{200}{1}$

2)2b - 3 = 7

$\longmapsto$ This equation has '=' sign and a variable 'b'

∴ It's an equation with a variable 'b'

$\rule{200}{1}$

3) (y - 7) > 5

$\longmapsto$ This doesn't have '=' sign .  [It's an inequality condition]

∴ It's not an equation with a variable.

$\rule{200}{1}$

4) 9/3 = 3

$\longmapsto$ This doesn't have any variable.

∴ It's not an equation with variable.

$\rule{200}{1}$

5) 7 × 3 - 19 = 2

$\longmapsto$ This doesn't have any variable.

∴ It's not an equation with variable.

$\rule{200}{1}$

Therefore,

Equations with a variable are,

$\longmapsto\bold{1) \ 17 + x = 5}\ \star \qquad\sf\left\{Variable : x \right\} \\\\ \\ \longmapsto\bold{2) \ 2b - 3 = 7} \ \star\qquad\sf\left\{Variable : b\right\}$

Answer 2

Given:

• 17 + x = 5
• 2b-3 =7
• (y-7) > 5
• 9/3 = 3
• 7× 3 - 19 = 2

━━━━━━━━━━━━━━━━

Need to find:

• Which are equations with variables?

━━━━━━━━━━━━━━━━

Solution:

• 1st option

17+ x = 5

▪It's an equation with a variable

▪ The variable = x

━━━━━━━━━━━

• 2nd Option

2b-3= 7

▪ It's an equation with variable

▪ The variable = b

━━━━━━━━━━━

• 3rd Option

(y - 7) > 5

▪ It's not an equation

━━━━━━━━━━━

• 4th option

9/3 = 3

▪ This equation don't have any variable

━━━━━━━━━━━

• 5th option

7 × 3 -19 = 2

▪ This equation don't have any variable.

━━━━━━━━━━━━━━━━━

Answer:

The equations with variables are:

▪ $\large{\red{\bold{\boxed{ 17 +x =5}}}}$ and

▪$\large{\red{\bold{\boxed{ 2b- 3 =7}}}}$

━━━━━━━━━━━━━━━

Knowledge cell:

• Equation is a statement that the values of two mathematical expressions are equal. It must have the sign "=" and not ">" or "<"

• Variables are not constant figures. They can be assigned with any value.