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Which of the following is an example of an equation with no solution?

(1 point)

• 3x + 4 = 4x + 3

• 4x + 3 = 3x + 3

03x + 4 = 3x + 4

03x +4=3x+3

9 answers

To determine which equation has no solution, we can solve each one:

  1. 3x + 4 = 4x + 3

    • Rearranging gives: \(3x - 4x = 3 - 4\)
    • This simplifies to: \(-x = -1\)
    • Therefore, \(x = 1\). (This has a solution)

  2. 4x + 3 = 3x + 3

    • Rearranging gives: \(4x - 3x = 3 - 3\)
    • This simplifies to: \(x = 0\). (This has a solution)

  3. 3x + 4 = 3x + 4

    • This equality holds for all values of \(x\), so it has infinitely many solutions (not applicable here as having no solution).

  4. 3x + 4 = 3x + 3

    • Rearranging gives: \(3x - 3x = 3 - 4\)
    • This simplifies to: \(0 = -1\), which is a contradiction. (This has no solution)

The equation with no solution is: 3x + 4 = 3x + 3.

Which of the following is an example of an equation with exactly one solution? (1 point)

03x+4= 3x+3

• 3x+4 = 3x+4

03x+4=4x+3

04x +3=4x+3

To find the equation with exactly one solution, we can analyze each option:

  1. 3x + 4 = 3x + 3

    • Rearranging gives: \(3x - 3x = 3 - 4\)
    • This simplifies to: \(0 = -1\), which is a contradiction. (This has no solution.)

  2. 3x + 4 = 3x + 4

    • This equality holds true for all values of \(x\), so it has infinitely many solutions. (Not applicable here.)

  3. 3x + 4 = 4x + 3

    • Rearranging gives: \(3x - 4x = 3 - 4\)
    • This simplifies to: \(-x = -1\)
    • Therefore, \(x = 1\). (This has exactly one solution.)

  4. 4x + 3 = 4x + 3

    • This equality also holds true for all values of \(x\), so it has infinitely many solutions. (Not applicable here.)

The equation with exactly one solution is: 3x + 4 = 4x + 3.

Solve for x to determine if the equation has one, none, or infinite solutions.
3(x+2) - 6 = 3x (1 point)

• The equation has no solution.

• The equation has one solution: x = -3.

• The equation has one solution: x = 3.

• The equation has infinite solutions.

Let's solve the given equation step by step:

Given:
\[ 3(x + 2) - 6 = 3x \]

  1. Distribute \(3\) on the left side: \[ 3x + 6 - 6 = 3x \]

  2. Simplify the left side: \[ 3x = 3x \]

At this point, we see that both sides of the equation are equal for all values of \(x\). This means the equation is true for any \(x\).

Thus, the equation has infinite solutions.

So, the correct answer is: The equation has infinite solutions.

Solve for x to determine if the equation has one, none, or infinite solutions.
4х =3 x+5) - 15 (1 point)
• The equation has no solution.
• The equation has one solution: 2 = 0.
• The equation has one solution: x = - 10.
• The equation has infinite solutions.

Let's solve the given equation step by step:

Given:
\[ 4x = 3x + 5 - 15 \]

  1. Simplify the right side: \[ 4x = 3x + 5 - 15 \] \[ 4x = 3x - 10 \]

  2. Subtract \(3x\) from both sides: \[ 4x - 3x = -10 \] \[ x = -10 \]

Now we've found that the equation has one solution: \(x = -10\).

So the correct answer is: The equation has one solution: x = -10.

Solve for x to determine if the equation has one, none, or infinite solutions.
5(2x + 2) - 7x=3x + 6 (1 point)

• The equation has one solution: x = 6.

• The equation has infinite solutions.

• The equation has one solution: x = 10.

• The equation has no solution.

Let's solve the equation step by step:

Given:
\[ 5(2x + 2) - 7x = 3x + 6 \]

  1. Distribute \(5\) on the left side: \[ 10x + 10 - 7x = 3x + 6 \]

  2. Combine like terms on the left side: \[ (10x - 7x) + 10 = 3x + 6 \] \[ 3x + 10 = 3x + 6 \]

  3. To isolate \(x\), subtract \(3x\) from both sides: \[ 10 = 6 \]

At this point, we see that \(10 = 6\) is a false statement. This indicates that there is no value for \(x\) that can satisfy the equation.

Thus, the equation has no solution.

So the correct answer is: The equation has no solution.