Question

find w. (2 points)
2(-6.4 + w) = 33.46
○ w = 2.6
○ w = 21.4
○ w = 23.13
○ w = -2.6

Explanation:

Step1: Divide both sides by 2

To isolate the term containing \( w \), we divide both sides of the equation \( 2(-6.4 + w)=33.46 \) by 2.
\( \frac{2(-6.4 + w)}{2}=\frac{33.46}{2} \)
Simplifying, we get \( -6.4 + w = 16.73 \).

Step2: Add 6.4 to both sides

To solve for \( w \), we add 6.4 to both sides of the equation \( -6.4 + w = 16.73 \).
\( -6.4 + w + 6.4 = 16.73 + 6.4 \)
Simplifying the left side (the -6.4 and +6.4 cancel) and the right side (16.73 + 6.4 = 23.13? Wait, no, wait: 16.73 + 6.4? Wait, no, wait, 33.46 divided by 2 is 16.73? Wait, no, 33.46 ÷ 2: 33 ÷ 2 = 16.5, 0.46 ÷ 2 = 0.23, so 16.5 + 0.23 = 16.73. Then 16.73 + 6.4: 16.73 + 6 = 22.73, 22.73 + 0.4 = 23.13? Wait, no, wait the options have 23.13? Wait, no, wait let's recalculate 33.46 ÷ 2: 33.46 / 2 = 16.73. Then 16.73 + 6.4: 16.73 + 6.4 = 23.13? Wait, but wait, maybe I made a mistake. Wait, no, let's check again. Wait, 221.4 = 42.8, which is not 33.46. Wait, 223.13 = 46.26, no. Wait, wait, no, wait the original equation: 2(-6.4 + w) = 33.46. Let's solve it correctly.

Wait, step 1: divide both sides by 2: -6.4 + w = 33.46 / 2 = 16.73. Then step 2: add 6.4 to both sides: w = 16.73 + 6.4 = 23.13? Wait, but the options include w=23.13. Wait, but let's check with the options. Wait, maybe I miscalculated 33.46 / 2. Wait, 33.46 divided by 2: 33 divided by 2 is 16.5, 0.46 divided by 2 is 0.23, so 16.5 + 0.23 = 16.73. Then 16.73 + 6.4: 16.73 + 6 = 22.73, 22.73 + 0.4 = 23.13. So w = 23.13. Wait, but let's check the options. The third option is w=23.13. Wait, but let's verify by plugging back in. 2(-6.4 + 23.13) = 2(16.73) = 33.46, which matches the original equation. So that's correct.

Wait, but earlier I thought maybe a miscalculation, but no, that's correct. So the steps are:

Step1: Divide both sides by 2

\( -6.4 + w = \frac{33.46}{2} = 16.73 \)

Step2: Add 6.4 to both sides

\( w = 16.73 + 6.4 = 23.13 \)

Answer:

\( w = 23.13 \) (corresponding to the option: \( w = 23.13 \))