Question

Verify and match the following types of solution to their correct equations:

• A. Unique solution
• B. Infinite solutions
• C. No solution

Answer 1

Given:
$\frac{1}{4}\left(32\text{x}\right)+11=8\text{x}-3+14$

Simplify: $\frac{1}{4}\times 32=8$

$⟹8\text{x}+11=8\text{x}-3+14$

$⟹8\text{x}+11=8\text{x}+11$

Subtract $11$ on both sides

$⟹8\text{x}+11-11=8\text{x}+11-11$

$⟹8\text{x}=8\text{x}$

The equation satisfies for any number.

$\therefore$ It has infinite solutions.

$13\text{x}+4+6=4\text{x}+11+9\text{x}$

Simplify: $4+6=10$

$⟹13\text{x}+10=4\text{x}+11+9\text{x}$

Simplify: $4\text{x}+9\text{x}=13\text{x}$

$⟹13\text{x}+10=13\text{x}+11$

Subtract 10 from both sides

$⟹13\text{x}+10-10=13\text{x}+11-10$

$⟹13\text{x}=13\text{x}+1$

Putting $\text{x}$ = 1, we get: $13=14$ ​​​​​
​
If the simplified form for an equation with no solution is a = b,
where a and b are two different numbers.

$\therefore$ It has no solution.

$33\text{x}+4=22\text{x}-6+10\text{x}$

Simplify: $22+10=32$

$⟹33\text{x}+4=32\text{x}-6$

Subtract $4$ from both sides

$⟹33\text{x}+4-4=32\text{x}-6-4$

Subtract $32\text{x}$ from both sides

$⟹33\text{x}-32\text{x}=32\text{x}-32\text{x}-10$

$⟹\text{x}=-10$

If the simplified form for an equation with unique solution is x = a,
where a is a numbers.​


$\therefore$ It has unique solution.