Answer:
<em> </em>14 x + 23 = 14 x - 23 has no solution ⇒ answer C
Step-by-step explanation:
* <em>Lets explain how to solve the problem</em>
- The equation has <em>NO</em> solutions if the variable in the equation
disappear and the left hand side (L.H.S) <em>not equal</em> the right hand
side (R.H.S)
- The equation has <em>infinite</em> solutions if the variable in the equation
disappear and the left hand side <em>equal</em> the right hand side
* <u><em>Now lets check which equation has no solution</em></u>
A) 14 x - 23 = 14 x - 23
- Add both sides by 23
∴ 14 x = 14 x
- Subtract 14 x from both sides
∴ 0 = 0
∵ L.H.S = R.H.S
∴ <em>The equation has infinite solutions</em>
<em />
B) -23 x - 14 = 14 x - 23
- Add both sides by 23
∴ -23 x + 9 = 14 x
- Add 23 x to both sides
∴ 9 = 37 x
- Divide both sides by 37
∴ x = 9/37
∴ <em>The equation has one solution</em>
<em />
C) 14 x + 23 = 14 x - 23
- Subtract 23 from both sides
∴ 14 x = 14 x - 46
- Subtract 14 x from both sides
∴ 0 = - 46
∵ L.H.S ≠ R.H.S
∴ <em>The equation has NO solutions</em>
<em />
D) -14 x + 23 = 14 x - 23
- Subtract 23 from both sides
∴ -14 x = 14 x - 46
- Subtract 14 x from both sides
∴ -28 x = - 46
- Divide both sides by -28
∴ x = 23/14
∴ <em>The equation has one solution</em>
<em />
<em>* </em><em> </em>14 x + 23 = 14 x - 23 has no solution