Question

How many solutions can be found for the linear equation? 4(x + 5) - 5 = 8x + 18/ 2

A)no solutions
B)one solution
C)two solutions
D)infinitely many solutions

Answer 1

Option A is correct

No solutions

Step-by-step explanation:

The distributive property says that:-

`a \cdot (b+c) = a\cdot b+ a\cdot c`

Given the equation:

`4(x+5)-5 = (8x+18)/(2)`

Using distributive property we have;

`4x+20-5 = (8x+18)/(2)`

⇒
`4x+15= (8x+18)/(2)`

Multiply both sides by 2 we have;

`8x+30 = 8x+18`

Subtract 8x from both sides we have;

`30=18` False.

For any value of x, there is no solutions for the given system of equation

Therefore, No solution can be found for the linear equation

Answer 2

Answer: The correct option is A.

Step-by-step explanation:

The given equation is,

`4(x+5)-5=(8x+18)/(2)`

Multiply both sides by 2.

`2[4(x+5)-5]=(8x+18)/(2)`

`8(x+5)+2(-5)=8x+18`

`8x+40-10=8x+18`

`8x+30=8x+18`

Subtract both sides by 8x.

`30=18`

This statement is false for any value of x, therefore the system of equation have no solution and option A is correct.