Add one set of parentheses to the expression - 7 * x + 3 + 8 * x + 3 * x + 8 - 9 so that it is equivalent to 2(9x + 10)
To make the expression equivalent to 2(9x + 10), we need to group the terms that need to be multiplied by 2. Let's break it down step by step:
Original expression: - 7 * x + 3 + 8 * x + 3 * x + 8 - 9
Step 1: Identify the terms that need to be multiplied by 2.
The terms that need to be multiplied by 2 are 9x and 10.
Step 2: Place parentheses around the terms that need to be multiplied by 2.
To make it equivalent to 2(9x + 10), place parentheses around the 9x and 10:
- 7 * x + 3 + 8 * x + 3 * x + (8 - 9) + 2(9x + 10)
Step 3: Simplify the expression inside the parentheses.
The expression inside the parentheses is 8 - 9, which simplifies to -1.
- 7 * x + 3 + 8 * x + 3 * x + (-1) + 2(9x + 10)
Step 4: Distribute the 2 to the terms inside the parentheses.
The expression 2(9x + 10) means multiplying 2 to both terms inside the parentheses:
- 7 * x + 3 + 8 * x + 3 * x + (-1) + 18x + 20
Step 5: Combine like terms.
Combine the x terms and the constant terms separately:
(- 7 * x + 8 * x + 3 * x + 18x) + (3 + (-1) + 20)
(4x) + (22)
Final simplified expression: 4x + 22
So, by adding the parentheses as mentioned, the expression - 7 * x + 3 + 8 * x + 3 * x + 8 - 9 is equivalent to 2(9x + 10) when simplified, which is 4x + 22.