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Finish the equation so that the equation has infinite amount of solutions. Click Here for Rubric 6 ( 7 + 2 ) − 8 = 6(7x+2)−8=

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
1 year ago

6(7x+2)−8=6(7x+2)−8

The equation is already complete and has an infinite number of solutions.

User Icon for Step-by-Step Bot Step-by-Step Bot answered
1 year ago

To create an equation with an infinite number of solutions, both sides of the equation must be equal. Therefore, we need to simplify the equation and eliminate any terms that would make the equation false.

Starting with the given equation:

6(7 + 2) - 8 = 6(7x + 2) - 8

First, simplify both sides of the equation by performing the operations inside the parentheses:

6(9) - 8 = 6(7x + 2) - 8

54 - 8 = 6(7x + 2) - 8

46 = 6(7x + 2) - 8

Next, eliminate the terms that would make the equation false. In this case, we can eliminate the constants (-8) on both sides:

46 + 8 = 6(7x + 2) - 8 + 8

54 = 6(7x + 2)

Now, we can divide both sides of the equation by the coefficient of the term in parentheses (6):

54/6 = (6(7x + 2))/6

9 = 7x + 2

To have an infinite number of solutions, the equation should be true regardless of the value of x. Since 9 = 7x + 2 is already solved for x, it means that any value of x that satisfies this equation would work.

Therefore, the equation 6(7 + 2) - 8 = 6(7x + 2) - 8 has an infinite number of solutions, and it can be expressed as:

9 = 7x + 2.

User Icon for Explain Bot Explain Bot answered
1 year ago

To create an equation with an infinite number of solutions, we need to ensure that both sides of the equation are equal, regardless of the value of the variable. In other words, every possible value for the variable should satisfy the equation.

Let's examine the given equation:
6(7x + 2) - 8 = ?

To ensure an infinite number of solutions, we can simplify the equation such that both sides cancel each other out.

Step 1: Distribute the 6 to the terms inside the parentheses:
42x + 12 - 8 = ?

Step 2: Combine like terms:
42x + 4 = ?

By choosing this specific equation, where the left side is equal to the right side, we guarantee that no matter the value of x, the equation will hold true. Therefore, the equation 42x + 4 = 42x + 4 has an infinite number of solutions.