Question

Sort each equation according to whether it has one solution, infinitely many solutions, or no solution.

Answer 1

Answer:

$5(x-2)=5x-7------\text{No\ solution}\\\\\\-3(x-4)=-3x+12------\text{Infinite\ many\ solution}\\\\\\4(x+1)=3x+4------\text{Unique\ solution}\\\\\\-2(x-3)=2x-6------\text{Unique\ solution}\\\\\\6(x+5)=6x+11------\text{No\ solution}$

Step-by-step explanation:

Unique solution--

We get a unique solution when on solving a equation we get a unique or single value of x.

Infinite-many solution--

We get a infinite many solution if on solving a equation the value of x is not determined uniquely but the equation is true for infinitely many values of x.

No solution--

We get a condition of no solution when on solving a equation we get a absurd condition.

1)

$5(x-2)=5x-7$

on solving the equation by using distributive property

$5\times x-5\times 2=5x-7\\\\\\5x-10=5x-7\\\\\\5x-5x=-7+10\\\\\\0=3$

which is a absurd condition.

Hence, the given equation has no solution.

2)

$-3(x-4)=-3x+12$

on solving the equation by using distributive property we get:

$-3\times x-3\times (-4)=-3x+12\\\\\\-3x+12=-3x+12$

As the expression on left and right hand side of the equation is same.

Hence, the equation will hold for infinite many values of x.

Hence, we get infinite many solution.

3)

$4(x+1)=3x-4$

on solving the equation:

$4\times x+4\times 1=3x+4\\\\\\4x+4=3x+4\\\\\\4x-3x=4-4\\\\\\x=0$

We get a unique value of x.

Hence, the equation has a unique solution.

4)

$-2(x-3)=2x-6$

on solving

$-2\times x-2\times (-3)=2x-6\\\\\\-2x+6=2x-6\\\\\\2x+2x=6+6\\\\\\4x=12\\\\\\x=3$

We get a unique value of x.

Hence, the equation has a unique solution.

5)

$6(x+5)=6x+11$

which is solved as follows:

$6\times x+6\times 5=6x+11\\\\\\6x+30=6x+11\\\\\\6x-6x=30-11\\\\\\0=19$

which is a absurd condition.

Hence, we get no solution.

Answer 2

《ANSWER》

《LINEAR EQUATIONS》

Solving all we get as

↪1) 5 (x -2) = 5x - 7

since after solving X is cancelled , NO SOLUTION

↪2) -3 (x - 4) = -3x + 12

SINCE after solving X is any value , infinitely many solutions

↪3) 4 (x + 1) = 3x + 4

solving we get as , 4x+ 4 = 3x + 4 =》 X =0

only one solution

↪4) -2 (x-3) = 2x - 6

Only one solution

↪5) 6 (x + 5) = 6x + 11

NO SOLUTION

All the equations are solved by the distributive law of algebra