Drag each equation to show if it could be a correct first step to solving the equation 2(x + 7) = 36
2x + 14 = 36
2x + 7 = 36
(2 · x) + 7 = 36
x + 7 = 18
2(x + 7) = 72
x + 14 = 36
Yes
No
Not Enough Information
Drag each equation to show if it could be a correct first step to solving the equation 2(x + 7) = 36 2x + 14 = 36 2x + 7 = 36 (2 · x) + 7 = 36 x + 7 = 18 2(x + 7) = 72 x + 14 = 36 Yes No Not Enough Information
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To determine if each equation is a correct first step to solving the equation (2(x + 7) = 36), we can consider the algebraic manipulation involved.
1. 2x + 14 = 36 – Yes: This comes from distributing (2) across (x + 7).
2. 2x + 7 = 36 – No: This does not correctly distribute the (2).
3. (2 · x) + 7 = 36 – No: It incorrectly adds (7) instead of distributing.
4. x + 7 = 18 – Yes: This is correct; if we first divide both sides of the original equation by 2, we get (x + 7 = 18).
5. 2(x + 7) = 72 – No: This alters the original equation incorrectly.
6. x + 14 = 36 – No: This is an incorrect manipulation.
So, the correct answers are:
– 2x + 14 = 36: Yes
– 2x + 7 = 36: No
– (2 · x) + 7 = 36: No
– x + 7 = 18: Yes
– 2(x + 7) = 72: No
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