Final answer:
After solving the original equation, 4x+20=90, to find x=17.5, we find that the equivalent equations are 1) 4(x + 5) = 90, 2) x + 5 = 22.5, and 5) 4x = 70.
Step-by-step explanation:
The question asks us to select all equations equivalent to 4x+20=90. Let's solve the given equation first:
4x + 20 = 90
4x = 90 - 20
4x = 70
x = 70/4
x = 17.5
Now, let's evaluate each option:
4(x + 5) = 90: This equation simplifies to 4x + 20 = 90, which is equivalent to the given equation.
x + 5 = 22.5: This simplifies to x = 17.5, which is the solution to the given equation, so it is also equivalent.
4(x + 20) = 90: Simplifying this equation would give us 4x + 80 = 90, which isn't equivalent to the initial equation.
x + 20 = 22.5: Simplifies to x = 2.5, which is not the solution we found for the given equation, so it is not equivalent.
4x = 70: This is already in the simplified form and is directly found from the given equation, making it equivalent.
Therefore, the equivalent equations to 4x + 20 = 90 are options 1, 2, and 5.