Question

consider the equation $42a - 26 = 436$.
9b
select the next step to solve for the variable.
given
$42a - 26 = 436$
$42a = 436 + 26$
add 26 to both sides of the equation
$\frac{42a}{42} = \frac{462}{42}$
$a = 11$
answer
options:
multiply both sides of the equation by 42
add 42 to both sides of the equation
subtract 42 from both sides of the equation
divide both sides of the equation by 42

Explanation:

After adding 26 to both sides to get \(42a = 462\), the next step to solve for \(a\) is to isolate \(a\). Since \(a\) is multiplied by 42, we need to divide both sides by 42. Looking at the options, the correct action is to divide both sides of the equation by 42 (though the option text says "Divide both sides of the equation by 12" which seems like a typo, but among the given options, the intended correct operation is dividing by 42, but if we go by the visible option with "Divide both sides of the equation by 42" (assuming the 12 is a typo), or if we check the steps, after \(42a = 462\), we do \(\frac{42a}{42}=\frac{462}{42}\) which is dividing both sides by 42. Wait, the options given: "Multiply both sides by 42" is wrong, "Add 42 to both sides" wrong, "Subtract 42" wrong, "Divide both sides by 12" (typo maybe, should be 42). But based on the equation \(42a = 462\), the next step is to divide both sides by 42. So the correct option (assuming the 12 is a typo) is the one with "Divide both sides of the equation by 42" (but in the image, one option is "Divide both sides of the equation by 12" which is incorrect, but maybe a typo. Wait, no, let's recheck. The equation after adding 26 is \(42a = 462\). To solve for \(a\), we divide both sides by 42. So the correct action is to divide both sides by 42. Among the options, if there's an option "Divide both sides of the equation by 42" (maybe the 12 is a typo in the image), then that's the answer. Alternatively, maybe the options are miswritten, but the mathematical step is dividing by 42.

Answer:

The correct next step is to divide both sides of the equation by 42 (corresponding to the option "Divide both sides of the equation by 42" – assuming the '12' is a typo in the image). If we strictly follow the options as given (with '12'), there's a typo, but the mathematical operation is dividing by 42. So the answer is the option with "Divide both sides of the equation by 42" (or the one with '12' as a typo).