Question

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

Answer 1

Answer:

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

Step-by-step 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.