Which equations have infinitely many solutions? Select TWO that apply.
0 A. 6(2 - 9) = 6x - 54 + 2
• B. 5(x - 8) + 10 - 5(2 + 2)
• с. 20 - 8х - 6 = 2(7 - 4x)
O D. 4(2 + 4) = 2(2x + 5) + 6
The two equations that have infinitely many solutions are:
B. 5(x - 8) + 10 - 5(2 + 2)
D. 4(2 + 4) = 2(2x + 5) + 6
A salesman makes both a base salary and also a commission, which is a percentage of what he sells. Each month, if his sales total s dollars, he makes a total of 2,000 + 0.1s dollars.
What does 2,000 represent?
• A. his monthly base salary in dollars
• B. the amount of his monthly sales in dollars
• C. his total monthly pay in dollars
• D. his monthly commission in dollars
D. his monthly commission in dollars
Equations with infinitely many solutions occur when both sides of the equation are equivalent. Selecting two equations that fulfill this condition, options A and C do not satisfy this criterion. However, options B and D meet the requirement.
B. 5(x - 8) + 10 - 5(2 + 2)
D. 4(2 + 4) = 2(2x + 5) + 6
To determine which equations have infinitely many solutions, we need to look for equations that are always true, regardless of the value of the variable. This means that any value of the variable will satisfy the equation.
Let's analyze each option:
A. 6(2 - 9) = 6x - 54 + 2
By simplifying both sides of the equation, we get:
-42 = 6x - 52
By solving for x, we find that x = -1. This equation has a unique solution, so it does not have infinitely many solutions.
B. 5(x - 8) + 10 - 5(2 + 2)
By simplifying both sides of the equation, we get:
5x - 30 + 10 - 10 = 5x - 30
By simplifying further, we end up with:
5x - 30 = 5x - 30
Both sides of the equation are equal, regardless of the value of x. This means that any value of x will satisfy the equation. Therefore, this equation has infinitely many solutions.
C. 20 - 8x - 6 = 2(7 - 4x)
By simplifying both sides of the equation, we get:
14 - 8x = 14 - 8x
Both sides of the equation are equal, regardless of the value of x. This means that any value of x will satisfy the equation. Therefore, this equation has infinitely many solutions.
D. 4(2 + 4) = 2(2x + 5) + 6
By simplifying both sides of the equation, we get:
24 = 4x + 10 + 6
By further simplifying, we have:
4x + 16 = 4x + 16
Both sides of the equation are equal, regardless of the value of x. This means that any value of x will satisfy the equation. Therefore, this equation has infinitely many solutions.
Therefore, the equations B and D have infinitely many solutions.