Given the equation 3x + 4 = 7, will there ever be more than one solution for x?
No because the value of x works out as 1
Because when your solving a quadratic equation your looking for x-intercepts which is where why equals 0 and x equals what ever the answer is.
Yes, when the inequality has a less that or equal to sign, or a greater than sign or equal to sign, then the equal sign can be replaced and get a solution that is common to both the equation and the inequality. There can also be other solutions to the inequality, where as the solution for the equation will be a valid one.
10
No. You have written two quantities. They can't be equal to each other AND also UNequal to each other.
Yes, of course. In this sense, it is a number just like any number. In general, an equation can have zero, one, or several solutions; the solutions can be positive, negative, zero, fractional, irrational, or complex, depending on the equation. Here is an equation that has zero as its solution: x = 0 (this is only an equality if your replace "x" with 0). Here are less trivial examples: x + 1 = 1 (the only solution is x = 0) x2 - x = 0 (two solutions: 0, and 1)
Because when your solving a quadratic equation your looking for x-intercepts which is where why equals 0 and x equals what ever the answer is.
panacea
Yes, when the inequality has a less that or equal to sign, or a greater than sign or equal to sign, then the equal sign can be replaced and get a solution that is common to both the equation and the inequality. There can also be other solutions to the inequality, where as the solution for the equation will be a valid one.
10
No - It will lead to a contradiction. No - It will lead to a contradiction.
This is part of Fermat's last theorem. He proposed that there was no solution to that equation (with whole numbers, at least) and wrote that he had a proof that he couldn't fit on the page he was using. He died without writing it down and mathematicians have been going nuts trying to rediscover it ever since. It has since been proven
No. You have written two quantities. They can't be equal to each other AND also UNequal to each other.
Yes, of course. In this sense, it is a number just like any number. In general, an equation can have zero, one, or several solutions; the solutions can be positive, negative, zero, fractional, irrational, or complex, depending on the equation. Here is an equation that has zero as its solution: x = 0 (this is only an equality if your replace "x" with 0). Here are less trivial examples: x + 1 = 1 (the only solution is x = 0) x2 - x = 0 (two solutions: 0, and 1)
See this example: x + 2 ≥ 4 x + 2 - 2 ≥ 4 - 2 x ≥ 2
a colliodal solution is heterogeneous..
Yes, but only when the inequality is not a strict inequality: thatis to say it is a "less than or equal to" or "more than or equal to" inequality. In such cases, the solution to the "or equal to" aspect will satisfy the corresponding inequality.
It has only one unique real root. There are some mathematical advantages in considering such a situation as two coincident real roots. However, given that you have to ask this question, you are still some way off getting to that level of maths - if you ever choose to do so.