Question

Which steps can be used to solve for the value of y? 2 3 (y + 57) = 178

a) Add 57 to both sides, then divide by 2 and 3.
b) Subtract 57 from both sides, then multiply by y and 3.
c) Invert both sides, multiply by 3, and subtract 57.
d) Divide by 2, subtract 57, and multiply by y.

Answer 1

To solve for y in the equation 2 x 3 (y + 57) = 178, divide both sides by 6 (2 x 3), then subtract 57 from both sides. The correct process is similar to option a given by the student, except the operations should be performed in reverse order.

Step-by-step explanation:

The student asked how to solve for y in the equation 2 × 3 (y + 57) = 178. The correct steps to solve for y involve performing algebraic operations in the reverse order of operations, which is often known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Here is the procedure:

• First, divide both sides by 2 and 3 to undo the multiplication.
• Next, subtract 57 from both sides to undo the addition inside the parentheses.
• Finally, you will have y isolated on one side of the equation and can identify its value.

The correct option that outlines these steps is: a) Add 57 to both sides, then divide by 2 and 3. However, this option contains a mistake in the order of operations; it should say 'Divide by 2 and 3, then subtract 57 from both sides'.