Question

question 1-3
select the expression equivalent to (8.4x + 2.9) + (-3.7x + 5).
-4.7x + 7.9
4.7x + 7.9
-12.1x + 7.9
12.1x + 7.9

Explanation:

Step1: Combine like terms for x

We have the expression \((8.4x + 2.9)+(-3.7x + 5)\). First, combine the \(x\)-terms: \(8.4x- 3.7x\).
\(8.4x-3.7x=(8.4 - 3.7)x = 4.7x\)? Wait, no, wait: Wait, 8.4 - 3.7? Wait, no, wait the second term is - 3.7x, so 8.4x+(-3.7x)=8.4x - 3.7x. Wait, 8.4 - 3.7 is 4.7? Wait, no, 8.4 - 3.7: 8.4 - 3 = 5.4, 5.4 - 0.7 = 4.7? Wait, no, wait 8.4 - 3.7: 8.4 - 3.7 = 4.7? Wait, no, 8.4 - 3.7 is 4.7? Wait, no, 8.4 - 3.7: 8 - 3 = 5, 0.4 - 0.7 = - 0.3, so 5 - 0.3 = 4.7? Wait, no, 8.4 - 3.7: 8.4 - 3.7 = 4.7? Wait, no, 8.4 - 3.7 = 4.7? Wait, 3.7 + 4.7 = 8.4? Yes, because 3 + 4 = 7, 0.7+0.7 = 1.4, 7 + 1.4 = 8.4. So 8.4x-3.7x = 4.7x? Wait, no, wait the original problem: Wait, the first parenthesis is (8.4x + 2.9), the second is (-3.7x + 5). Wait, maybe I made a mistake. Wait, 8.4x + (-3.7x) = (8.4 - 3.7)x = 4.7x? Wait, no, 8.4 - 3.7 is 4.7? Wait, 8.4 - 3.7: 8.4 - 3 = 5.4, 5.4 - 0.7 = 4.7. Yes. Then the constant terms: 2.9 + 5 = 7.9. Wait, but that's not matching. Wait, wait the options: Wait, maybe I misread the first term. Wait, the first term is (8.4x + 2.9) or (8.4x + 2.9)? Wait, no, the user's problem: (8.4x + 2.9) + (-3.7x + 5). Wait, 8.4x - 3.7x = 4.7x? Wait, no, 8.4 - 3.7 is 4.7? Wait, 8.4 - 3.7: 8.4 - 3.7 = 4.7. Then 2.9 + 5 = 7.9. So the expression would be 4.7x + 7.9? But that's option B? Wait, no, wait the options: Wait, the options are:

• -4.7x +7.9

• 4.7x +7.9

• -12.1x +7.9

• 12.1x +7.9

Wait, no, wait I think I made a mistake in the sign. Wait, the second parenthesis is (-3.7x + 5), so when we remove the parentheses, it's 8.4x + 2.9 - 3.7x + 5. Now, combine x terms: 8.4x - 3.7x. 8.4 - 3.7 = 4.7? Wait, 8.4 - 3.7: 8.4 - 3 = 5.4, 5.4 - 0.7 = 4.7. So 4.7x. Then constants: 2.9 + 5 = 7.9. So the expression is 4.7x + 7.9, which is the second option. Wait, but let me check again. Wait, 8.4x - 3.7x: 8.4 - 3.7 = 4.7, so 4.7x. Then 2.9 + 5 = 7.9. So the equivalent expression is 4.7x + 7.9, which is the second option (the one with 4.7x +7.9).

Wait, but maybe I misread the first term. Wait, the original problem: (8.4x + 2.9) + (-3.7x + 5). Wait, 8.4x - 3.7x = 4.7x, 2.9 + 5 = 7.9. So the answer is 4.7x +7.9, which is the second option.

Step2: Combine constant terms

Now, combine the constant terms: \(2.9 + 5\).
\(2.9+5 = 7.9\)

Step3: Write the combined expression

Putting the combined \(x\)-terms and constant terms together, we get \(4.7x + 7.9\).

Answer:

4.7x + 7.9 (the second option, which is "4.7x + 7.9")