All categories

3 years ago

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

Mathematics

2 answers:

loris [4]3 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]3 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

You might be interested in

Blake measures the lengths, in inches, of 10 insects. He records the lengths of the insects on this line plot. He adds the lengt

ivanzaharov [21]

Answer: 5 inches

Step-by-step explanation:

The x's denote the insects measured so the longest insects would be of lengths:

1³/₄ inch, 1³/₄ inch and 1¹/₂ inch.

Adding them together would require converting them to improper fractions first:

7/4, 7/4, 3/2

Pick a denominator that is both denominators' lowest common multiple = 4

Adding them:

Divide the LCM by the denominator of the fraction and multiply the result by the numerator:

= (7 + 7 + 6) / 4

= 20/4

= 5 inches

7 0

3 years ago

Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal plac

vredina [299]

$-1\le\sin\theta\le1\implies(\csc\theta\le-1)\cup(\csc\theta\ge1)$

which means $\csc\theta=0$ has no solution, and we can omit that factor.

This leaves us with

$2\cos\theta-1=0\implies\cos\theta=\dfrac12$

which occurs for $\theta=\pm\dfrac\pi3+2n\pi$ .