Question

Select all the equations that have no solution and state your reasoning as of "why" they do not have a solution. +6=5+ x+6=5+x −2(−3)=-2+6 −2(x−3)=-2x+6 4−4=3+2 4−4x=3x+2 4(+1)=3(+2) 4(x+1)=3(x+2) 5−3=-3+4 5−3x=-3x+4

Answer 1

Equations:

$x+6=5+x$

$-2(x-3)=-2x+6$

$4-4x=3x+2$

$4(x+1)=3(x+2)$

$5-3x=-3x+4$

Answer:

$x+6=5+x$

$5-3x=-3x+4$

Step-by-step explanation:

Given

$x+6=5+x$

$-2(x-3)=-2x+6$

$4-4x=3x+2$

$4(x+1)=3(x+2)$

$5-3x=-3x+4$

Required:

Which have no solution

$x+6=5+x$

Subtract x from both sides

$x -x+6 = 5 + x - x$

$6 = 5$

$x+6=5+x$ has no solution because $6 \ne 5$

$-2(x-3)=-2x+6$

Open bracket

$-2x + 6 = -2x + 6$

Both sides are equal.

Hence, there is an $Infinite\ Number$ of Solutions

$4-4x=3x+2$

Collect like terms

$-3x - 4x = 2 - 4$

$-7x = -2$

Solve for x

$x = \frac{-2}{-7}$

$x = \frac{2}{7}$ --- This has a solution

$4(x+1)=3(x+2)$

Open brackets

$4x + 4 = 3x + 6$

Collect like terms

$4x-3x = 6 - 4$

$x = 2$ --- This has a solution

$5-3x=-3x+4$

Add 3x to both sides

$5 - 3x + 3x = -3x + 3x + 4$

$5 = 4$

$5-3x=-3x+4$ has no solution because $5 \ne 4$