Let’s figure out unknown weights on balanced hangers.
Illustrative Math Unit 8.4, Lesson 3 (printable worksheets)
An equation tells us that two expressions have equal value. For example, if 4x + 9 and -2x - 3 have equal value, we can write the equation
4x + 9 = -2x - 3
Earlier, we used hangers to understand that if we add the same positive number to each side of the equation, the sides will still have equal value. It also works if we add negative numbers! For example, we can add -9 to each side of the equation.
4x + 9 + -9 = -2x - 3 + -9 (add -9 to each side)
4x = -2x - 12 (combine like terms)
Since expressions represent numbers, we can also add expressions to each side of an equation. For example, we can add 2x to each side and still maintain equality.
4x + 2x = -2x - 12 + 2x (add 2x to each side)
6x = -12
If we multiply or divide the expressions on each side of an equation by the same number, we will also maintain the equality (so long as we do not divide by zero).
6x • 1/6 = 12 • 1/6 (multiply each side by 6)
Now we can see that x = -2 is the solution to our equation.
We will use these moves in systematic ways to solve equations in future lessons.
Figures A, B, C, and D show the result of simplifying the hanger in Figure A by removing equal weights from each side.
Your teacher will give you some cards. Each of the cards 1 through 6 show two equations. Each of the cards A through E describe a move that turns one equation into another.
In a cryptarithmetic puzzle, the digits 0–9 are represented with letters of the alphabet. Use your understanding of addition to find which digits go with the letters A, B, E, G, H, L, N, and R.
HANGER + HANGER + HANGER = ALGEBRA
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