Question

Question

Which of the following equations has infinite solutions?(1 point)
Responses

−10x+4=10x+3
−
10
x
+
4
=
10
x
+
3
negative 10 x plus 4 equals 10 x plus 3

10x+3=−10x+3
10
x
+
3
=
−
10
x
+
3
10 x plus 3 equals negative 10 x plus 3

−10x+4=−10x+4
−
10
x
+
4
=
−
10
x
+
4
negative 10 x plus 4 equals negative 10 x plus 4

10x+4=10x−4

Answer 1

To determine which equation has infinite solutions, we need to examine each option. An equation has infinite solutions if it simplifies to an identity (e.g., a statement that is always true).

1. Equation: \(-10x + 4 = 10x + 3\)

   • Rearranging gives: \(-20x + 4 = 3\)
   • This simplifies to \( -20x = -1\) or \( x = \frac{1}{20}\). (One unique solution)

2. Equation: \(10x + 3 = -10x + 3\)

   • Rearranging gives: \(20x = 0\)
   • This simplifies to \( x = 0\). (One unique solution)

3. Equation: \(-10x + 4 = -10x + 4\)

   • This is an identity because both sides are always equal for any value of \(x\). (Infinite solutions)

4. Equation: \(10x + 4 = 10x - 4\)

   • Rearranging gives: \(4 = -4\), which is false. (No solutions)

From the above analysis, the equation that has infinite solutions is:

\(-10x + 4 = -10x + 4\).