Subjects algebra

Shape Equation F10D58

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1. **Stating the problem:** We have three rows of shapes representing an algebraic equation. Each shape corresponds to a variable: let the square be $S$, the triangle be $T$, and the circle with a "Q" be $Q$. 2. **Writing the algebraic expressions for each row:** - First row: 3 squares + 1 triangle + 3 squares $= 3S + T + 3S = 6S + T$ - Second row: 5 squares + 1 triangle + 1 circle $= 5S + T + Q$ - Third row: 4 squares + 3 circles $= 4S + 3Q$ 3. **Forming the equation:** Since these rows are part of a model, we assume the sums are equal: $$6S + T = 5S + T + Q = 4S + 3Q$$ 4. **Solving the system:** From the first equality: $$6S + T = 5S + T + Q$$ Subtract $T$ from both sides: $$6S + \cancel{T} = 5S + \cancel{T} + Q$$ Simplify: $$6S = 5S + Q$$ Subtract $5S$ from both sides: $$6S - 5S = Q$$ $$S = Q$$ 5. From the second equality: $$5S + T + Q = 4S + 3Q$$ Subtract $4S$ from both sides: $$5S - 4S + T + Q = 3Q$$ Simplify: $$S + T + Q = 3Q$$ Subtract $Q$ from both sides: $$S + T = 2Q$$ Substitute $S = Q$: $$Q + T = 2Q$$ Subtract $Q$: $$T = Q$$ 6. **Final solution:** $$S = Q, \quad T = Q$$ All variables are equal. **Answer:** $S = T = Q$