Question

For the equation 2(4x+10)=8x+k what value of k will create infineltly many solutions please help

Answer 1

The value of k = 20 for equation 2(4x+10)=8x+k to have infinitely many solutions.

Explanation:

Given the expression

`2(4x+10)=8x+k`

solving

`2(4x+10)=8x+k`

`8x+20 = 8x+k`

We know that the equations with infinitely many solutions have the same expressions on both sides

It means the value of k can be determined by further simplifying such as

`8x+20 = 8x+k`

8x+20-8x = k

20 = k

Therefore, the value of k = 20 for equation 2(4x+10)=8x+k to have infinitely many solutions.

VERIFICATION:

Given

`2(4x+10)=8x+k`

`8x+20 = 8x+k`

Put k = 20 in the equation

`8x+20 = 8x+20`

`8x+20 - 8x+20 = 0`

`0 = 0`

equations with infinitely many solutions have the same expressions on both sides.

This means the statement is always true.