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2 years ago

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

Mathematics

2 answers:

loris [4]2 years ago

8 0

<h2>Answer:</h2>

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

<h2>Step-by-step explanation:</h2>

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.

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

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.

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

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.

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

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.

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

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.

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

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.

Aliun [14]2 years ago

5 0

《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

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