the equation is : - (2x + 3)-(4 + x).
Using the distributive property, my friend got the answer -7 - 3x. I have been fiddling with this problem for 3 hours and don't understand how he got this answer. Can someone please thoroughly explain this to me?
- (2x + 3)-(4 + x).
Check my work.
remove the parentheses.
-2x-3-4-x=
combine terms.
-3x-7
thanxxx so much. awesome help!!
Of course! I'll be glad to explain the solution step by step.
The given equation is: - (2x + 3) - (4 + x).
To simplify this equation using the distributive property, we need to multiply the negative sign outside the parentheses by every term inside the parentheses.
Let's break down the steps:
Step 1: Distribute the negative sign to the terms inside the first set of parentheses: - (2x + 3).
- The negative sign outside the parentheses changes the signs of both terms inside.
- So, it becomes: -2x - 3.
Step 2: Distribute the negative sign to the terms inside the second set of parentheses: - (4 + x).
- The negative sign outside the parentheses changes the signs of both terms inside.
- So, it becomes: -4 - x.
Now, we can rewrite the equation with the distributed terms:
-2x - 3 - (-4 - x).
Next, let's simplify further:
Step 3: Remove the double negative by changing the signs of the terms inside the second set of parentheses. (-1) * (-4) = 4 and (-1) * (-x) = x. So, it becomes: -2x - 3 + 4 + x.
Step 4: Group the like terms together. In this case, we have two terms with 'x' and two constants.
- Grouping together the 'x' terms: -2x + x = -x.
- Grouping together the constant terms: -3 + 4 = 1.
Step 5: Rewrite the equation with the simplified terms:
-x + 1.
Therefore, the simplified expression using the distributive property is -x + 1.
It seems like your friend made an error in their calculation. The correct answer should be -x + 1, not -7 - 3x.