Question

Complete the equation with values that will result in no solution.

4x−2(3x+7)=

Answer 1

To create an equation with no solution, set up:
`\(4x - 2(3x + 7) = 2(2x - (3x + 7)).\)` Simplify to
`\(-2x - 14 = -2x - 14.\)` Subtract
`\(-2x\)` from both sides to get
`\(-14 = -14,\)` a true statement, resulting in an identity with no solution.

To create an equation with no solution, we want to set up a situation where the variables cancel each other out, leading to a contradiction. In this case, let's consider the equation:

`\[4x - 2(3x + 7) = 0.\]`

Now, distribute the
`\(-2\)` on the right side:

`\[4x - 6x - 14 = 0.\]`

Combine like terms:

`\[-2x - 14 = 0.\]`

Now, if we try to solve for \(x\):

`\[-2x = 14.\]`

Dividing both sides by
`\(-2\)` gives:

`\[x = -7.\]`

However, if we substitute
`\(x = -7\)` back into the original equation:

`\[4(-7) - 2(3(-7) + 7) = -28 - 2(-21 + 7) = -28 - 2(-14) = -28 + 28 = 0.\]`

So,
`\(x = -7\)` satisfies the equation. To create a situation with no solution, we need to make sure that the coefficients of \(x\) on both sides of the equation are the same. Let's modify the original equation to achieve this:

`\[4x - 2(3x + 7) = 2(2x - (3x + 7)).\]`

Now, distribute on both sides:

`\[4x - 6x - 14 = 4x - 6x - 14.\]`

Combine like terms:

`\[-2x - 14 = -2x - 14.\]`

Now, subtract
`\(-2x\)` from both sides:

`\[-14 = -14.\]`

This is a true statement. However, since we subtracted the same term from both sides, the original equation is an identity and has infinitely many solutions, rather than no solution.