Lucy has a lemonade stand. The table shows Lucy’s profits when she sells different amounts of lemonade.​Which equation could Lucy use to determine her profit, , when she sells cups of lemonade?

x = 2

Step-by-step explanation:

First translate the image into an equation using the key. Once you do that, your equation should look like this:

(x + x + x) + (-1 + -1 + -1 + -1 + -1) = (-x + -x) + (1 + 1 + 1 + 1 + 1)

3x - 5 = -2x + 5

(given)

3x - 5 = -2x + 5

+5. +5

(addition property of equality)

*cancel out -5 on the left hand side, and isolate it from x by adding +5 on each side*

3x = -2x + 10

+2x +2x

(addition property of equality)

*cancel out the negative 2x, and isolate it from the constant term on the right hand side by adding 2x on both sides*

5x = 10

÷5. ÷5

(division property of equality)

*divide by 5(GCF) on both sides to isolate

x by itself*

x = 2

If you want to test this solution, substitute this back into the equation.

x = 2 → 3x - 5 = -2x + 5. 3(2) - 5 = -2(2) + 5 = 6 - 5 = -4 + 5 = 1 = 1