Enter the numbers that make the algebraic expressions equivalent. Expression 1: 4x+5(x−2)+__. Expression 2: __x−11−x+9.
To make the algebraic expressions equivalent, we need to find the missing numbers that make both expressions equal.
Expression 1: 4x + 5(x−2) + __
Expression 2: __x − 11 − x + 9
To find the missing numbers, let's expand the parenthesis in Expression 1:
4x + 5x - 10 + __
Now we can simplify Expression 1 further:
9x - 10 + __
For the two expressions to be equivalent, the terms with x in both expressions must be equal. So we can set them equal to each other:
9x - 10 + __ = __x - 11 - x + 9
Simplifying this equation:
9x - 10 + __ = -x - 2
We now have an equation with two unknowns. To solve for the missing numbers, we need another equation. Let's compare the constant terms in both expressions:
-10 + __ = -2
Simplifying this equation gives:
__ = -2 + 10
__ = 8
Therefore, to make the algebraic expressions equivalent:
Expression 1: 4x + 5(x−2) + 8
Expression 2: 8x − 11 − x + 9