3. Which of the following equations has an infinite number of solutions?

3x - 3 + -4x

2y+ 4 -y = 16

7x + 5 = 4x + 5 + 3x

6y -2 =2 (y-1)

Write the inequality and solve for the following problem:

The result of 6 subtracted from a number n is at least 2

n - 2>6; n > 8

n-6>2; n > 8

n + 6 > 2; n < 4

n + 6> 2; n> 4

7x + 5 = 4x + 5 + 3x yields 0=0 infinite sols

n-6>2
add 6 to both sides
n > 8

Thanks!

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To determine which equation has an infinite number of solutions, we need to solve each equation and see if we end up with the same value on both sides of the equation, indicating that the equation is true for any value of the variable.

Let's start with the given equations:

1) 3x - 3 + -4x

Combine like terms: -x - 3

This equation simplifies to -x - 3 = 0, which means the equation is not true for all values of x. Thus, it does not have an infinite number of solutions.

2) 2y + 4 - y = 16

Combine like terms: y + 4 = 16

Subtract 4 from both sides: y = 12

This equation has a specific solution for y, which means it does not have an infinite number of solutions.

3) 7x + 5 = 4x + 5 + 3x

Combine like terms: 7x + 5 = 7x + 5

This equation simplifies to 7x + 5 = 7x + 5, which means both sides are equal for any value of x. Thus, this equation has an infinite number of solutions.

4) 6y - 2 = 2(y - 1)

Distribute 2 on the right side: 6y - 2 = 2y - 2

Combine like terms: 6y - 2 - 2y = -2

Simplify: 4y - 2 = -2

Add 2 to both sides: 4y = 0

Divide both sides by 4: y = 0

This equation has a specific solution for y, which means it does not have an infinite number of solutions.

Therefore, the equation 7x + 5 = 4x + 5 + 3x has an infinite number of solutions.

Now let's move on to solving the inequality:

The inequality states that "The result of 6 subtracted from a number n is at least 2."

To translate this into an inequality, we subtract 6 from both sides of the equation:

n - 6 ≥ 2

This gives us the inequality n ≥ 8, which means that the variable n must be greater than or equal to 8 in order for the result of subtracting 6 from n to be at least 2.

So the correct inequality for this problem is n ≥ 8.