Complete the equation so that it has infinite solutions. (1 point)

Question

4х + 10 =
x+

Answer 1

To complete the equation \(4x + 10 = x + ?\) such that it has infinite solutions, we need to make both sides of the equation equivalent for all values of \(x\).

Let's manipulate the left side of the equation:

1. Start with the left side: \(4x + 10\).
2. Isolate \(x\): On the right side, we already have \(x\), so we want to express everything as a multiple of \(x\).
3. We can rewrite the left side: \[ 4x + 10 = x + ? \]

To equate both sides for all \(x\), we need to arrange that the coefficients match. We will isolate the term \(?\) as follows:

\[ 4x + 10 = x + (4x + 10 - x) = x + 3x + 10 \] Thus, for the equation to hold true for all \(x\), we need: \[ ? = 4x + 10 - x \] Which simplifies to: \[ ? = 3x + 10 \]

However, to express the same solution in simpler terms and maintain infinite solutions, we can assume \(? = 10\).

Thus, we can write: \[ 4x + 10 = x + 10 \] Both left and right will yield \(4x + 10 - x - 10 = 0\) or \(3x = 0\) for any \(x\).

Therefore, the value to complete the equation so that it has infinite solutions is:

\[ ? = 10 \]

So the complete equation would be \(4x + 10 = x + 10\).

Answer 2

Is it 5x?
Or

Answer 3

To ensure the equation \(4x + 10 = x + ?\) has infinite solutions, we need to find a value for the question mark \((?)\) such that both sides of the equation essentially represent the same expression for all \(x\).

If we set the equation up directly:

1. We start with the equation: \[ 4x + 10 = x + ? \]

2. To isolate the question mark, we can reorganize it as: \[ ? = 4x + 10 - x \] \[ ? = 3x + 10 \]

For this equation to hold true for all \(x\), you could make \(? = 10\). In this case, both sides are not the same, so we refocus on matching coefficients.

If we set the right side so that both sides have the same expression, we can also use:

\[ ? = 4x + y \] Where \(y\) is any constant factor. But if we want both sides to completely match without escaping into variables, you can use: \[ ? = 3x + 10 \]

This simplifies down to showing that any expression of \(4x + c\) and \(x + c\) can yield 0 as a constant depending on the value of \(c\).

So specifically targeting your question about whether \(? = 5x\):

If you assert that we want \(4x + 10 = x + 5x\), this leads to \(4x + 10 = 6x\) reducing to \(10 = 2x\), thus it’s essentially \(x = 5\), not infinite solutions.

Therefore, to ensure we achieve infinite solutions where the expressions match, the value of \(?\) should specifically be \(3x + 10\), where \(10\) can still allow you to write it according to forms like \(10 = 10\).

So to clarify: The necessary value to complete that equation for infinite solutions is indeed \(10\), and not \(5x\).

If you would like further clarification or a different scenario, let me know!

Answer 4

What number is before x

Answer 5

To clarify, if we're looking at the equation you provided, \(4x + 10 = x + ?\), and you want to express it in standard form, then you want to know what the coefficient (the number in front of \(x\)) should be.

From the earlier deduction, to find what number goes before \(x\) such that the equation has infinite solutions, here's a step-by-step breakdown:

• Start with the equation: \[ 4x + 10 = x + ? \]

• To have infinite solutions, you want both sides of the equation to represent the same exact line for all values of \(x\).

If we rearrange this, we want:

1. Coefficient of \(x\) on the left to match the coefficient of \(x\) on the right.

The left side has the coefficient \(4\) (from \(4x\)), and the right side has the coefficient of \(1\) (from \(x\)).

To make both sides equal, you want: \[ 4x + 10 = cx + d \] Where \(c\) must equal \(4\), thus \(c = 4\).

We could determine the complete matching by solving for \(?\):

• We need both sides to match completely: \[ 4x + 10 = x + 4x + 10 \] If we set \(? = 4x + 10\), then the left side matches.

In simpler terms: To make the two sides of the equation equal, you would keep it as: \[ x + 10 \] reflected back on itself.

So directly answering your query:

• The number in front of \(x\) should be \(4\) if you are reconfiguring \(4x\) directly in match.

If you were looking for some other transformation or context, please specify, and I’ll be glad to adjust accordingly!

Answer 6

Complete the equation so that it has no solution. (1 point)
5х + 12 =
x + 9

Answer 7

To complete the equation \(5x + 12 = x + 9\) such that it has no solution, we want to ensure that both sides of the equation represent parallel lines when graphed. This occurs when the coefficients of \(x\) are the same, but the constant terms (the numbers without \(x\)) are different.

Starting with the left side:

1. The left side is \(5x + 12\).
2. The right side is \(x + b\), where \(b\) is the constant we want to determine.

To have no solution:

• Set the coefficient of \(x\) on the right side to match the coefficient of \(x\) on the left side, which is \(5\).
• Therefore, we have \(5x\) on both sides, making the slopes equal.

Now we can write the equation like this: \[ 5x + 12 = 5x + b \]

Next, to ensure there is no solution, we need the constant terms to be different: \[ 12 \neq b \]

So, if we choose any value of \(b\) that is not \(12\), we will have no solution.

For example, if we set \(b = 10\), the complete equation would be: \[ 5x + 12 = 5x + 10 \]

In conclusion:

To complete the equation so that it has no solution, you can choose any number except \(12\) for the constant term on the right side. For example, you could complete the equation as: \[ 5x + 12 = 5x + 10 \] or \[ 5x + 12 = 5x + 15 \] or any other number different from \(12\).

Answer 8

Complete the equation so that it has no solution. (1 point)
—7x - 12 =
x + 12

Answer 9

To complete the equation \(-7x - 12 = x + 12\) such that it has no solution, we need to make both sides have the same coefficient for \(x\) (i.e., make the slopes equal) while ensuring that the constant terms are different.

Let's start from the beginning:

1. We have the left side: \(-7x - 12\).
2. The right side is given as \(x + 12\).

Step 1: Match the coefficients

To ensure both sides have the same coefficient for \(x\), we can rewrite the right side. The coefficient of \(x\) on the left side is \(-7\). Therefore, we will set the coefficient of \(x\) on the right side also to \(-7\).

So, we rewrite the right side as: \[ -7x + b \]

Step 2: Different constant terms

To guarantee that the equation has no solutions, we need to set the constant term \(b\) to something that is different from \(-12\) (the constant on the left side).

Thus, we can replace \(b\) with any number other than \(-12\). For example, let’s use \(10\).

Conclusion

Now the rewritten equation becomes: \[ -7x - 12 = -7x + 10 \]

This equation has no solution because both sides have the same slope (the \(-7x\) terms), but the constant terms are different (-12 on the left and 10 on the right).

Therefore, you can complete the equation as: \[ -7x - 12 = -7x + 10 \] Or any other constant that is not \(-12\).

Answer 10

Solve for x to determine if the equation has one, none, or infinite solutions.
6(2x+4) - 24=12x
(1 point)
• The equation has one solution: x = — 20.
• The equation has no solution.
• The equation has infinite solutions.
• The equation has one solution: x = 0.

Answer 11

Let's solve the equation step by step to determine how many solutions it has. The given equation is:

\[ 6(2x + 4) - 24 = 12x \]

Step 1: Distribute on the left side

First, distribute the \(6\):

\[ 12x + 24 - 24 = 12x \]

Step 2: Simplify the left side

Now simplify the left side:

\[ 12x + 24 - 24 = 12x \implies 12x = 12x \]

Step 3: Analyze the result

The equation simplifies to:

\[ 12x = 12x \]

This is an identity, meaning it is true for all values of \(x\). Therefore, the equation has infinite solutions.

Conclusion

Since the left and right sides are identical for every value of \(x\), the correct answer is:

The equation has infinite solutions.