If doubling a number and adding 20 to the result gives the same answer as multiplying the number by 8 and taking away 4 from the product, the number is

### Concept & Logic This word problem straightforwardly describes an equality between two distinct operations performed on the same initial unknown variable. $$ 2x + 20 = 8x - 4 $$ ### Step-by-Step Solution * Let the unknown number be $x$. * Operation 1: Doubling the number and adding 20 yields: $$ 2x + 20 $$ * Operation 2: Multiplying the number by 8 and taking away 4 yields: $$ 8x - 4 $$ * The problem states these two operations give the same answer: $$ 2x + 20 = 8x - 4 $$ * Group the variable terms on one side by subtracting $2x$ from both sides: $$ 20 = 6x - 4 $$ * Add 4 to both sides: $$ 24 = 6x $$ * Divide by 6 to isolate $x$: $$ x = \frac{24}{6} = 4 $$ ### Exam Strategy & Shortcut This question can be answered extremely quickly using the **Option Elimination Method**. * Test (a) 2: $(2 \times 2) + 20 = 24$. $(2 \times 8) - 4 = 12$. Not equal. * Test (c) 4: $(4 \times 2) + 20 = 28$. $(4 \times 8) - 4 = 28$. They match! For simple linear equations with small integer options, substituting the answers directly is often faster than writing out the algebraic steps. ### Common Pitfall When reading "taking away 4 from the product", some students mistakenly write $4 - 8x$ instead of $8x - 4$. Order matters in subtraction; always subtract the specified amount *from* the base value. ### Final Answer **Therefore, the correct answer is 4.**