Questions: Which of the following expressions is equivalent to 13x-21 for all numbers x? 10(x-1)-11 13(x-21) 3(x-21)+10x 3(x+7)+13x 3(x-7)+10x

Transcript text: Which of the following expressions is equivalent to $13 x-21$ for all numbers $x$ ? $10(x-1)-11$ $13(x-21)$ $3(x-21)+10 x$ $3(x+7)+13 x$ $3(x-7)+10 x$

Solution

Solution Steps

Step 1: Analyze the Given Expression

The expression we need to find an equivalent for is $13x - 21$.

Step 2: Evaluate Each Option

Let's evaluate each option to see which one simplifies to $13x - 21$.

Option 1: $10(x-1)-11$
\[ 10(x-1) - 11 = 10x - 10 - 11 = 10x - 21 \] This simplifies to $10x - 21$, which is not equivalent to $13x - 21$.
Option 2: $13(x-21)$
\[ 13(x-21) = 13x - 273 \] This simplifies to $13x - 273$, which is not equivalent to $13x - 21$.
Option 3: $3(x-21)+10x$
\[ 3(x-21) + 10x = 3x - 63 + 10x = 13x - 63 \] This simplifies to $13x - 63$, which is not equivalent to $13x - 21$.
Option 4: $3(x+7)+13x$
\[ 3(x+7) + 13x = 3x + 21 + 13x = 16x + 21 \] This simplifies to $16x + 21$, which is not equivalent to $13x - 21$.
Option 5: $3(x-7)+10x$
\[ 3(x-7) + 10x = 3x - 21 + 10x = 13x - 21 \] This simplifies to $13x - 21$, which is equivalent to the given expression.