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Fill in the gap for the given equation to have:No solutionsOne solutionInfinitely many solutions

Fill In The Gap For The Given Equation To HaveNo SolutionsOne SolutionInfinitely Many Solutions class=

Sagot :

Answer:

No solutions: 6 - 3 + 4x = 4 x + 4

One solution: 6 - 3 + 4x = 3 x + 4

Infinitely many solutions: 6 - 3 + 4x = 4 x + 3

Explanations:

We are to provide a value into the gap, theat will make the equation have:

1. No solutions

2. infinitely many solutions

3. One solution

The given equation is:

6 - 3 + 4x = ...... x + .........

1. No solutions:

Note that for an equation to have no solution, the Right Hand Side should not be equal to the Left Hand Side after simplification.

Therefore, for the equation 6 - 3 + 4x = ...... x + .........

By simplifying the equation:

3 + 4x = ...... x + .........

For the equation to not have solution, put 4 in the first gap, and a number that isn't 4 in the second gap.

3 + 4x = 4x + 4

3 + 4x - 4x = 4

3 = 4 ( False)

Since this is false, the equation 3 + 4x = 4x + 4 is unsolvable:

2. One solution:

For the equation to have one solution, the coefficient of x on the right and left sides must not be the same.

3 + 4x = ...... x + .........

For the equation to have just one solution the coefficient of x on the right hand side must take on a value that is not 4, (e.g. 3), the second gap can take on any value. The constant can take on any value

3 + 4x = 3x + 4

4x - 3x = 4 - 3

x = 1

3. Infinitely many solutions:

Note that for an equation to have infinitely many solutions, the Right Hand Side should be equal to the Left Hand Side after simplification.

6 - 3 + 4x = ...... x + .........

3 + 4x = ...... x + .........

The coefficient of x on the Left hand side has to be 4, and the constant has to be 3 to make the Left Hand Side equal to the Right hand side.

3 + 4x = 4x + 3

3 + 4x - 4x = 3

3 + 0 = 3

3 = 3 (True)

Since LHS = RHS, the given equation has infinitely many solutions.

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