Final answer:
To solve the equation 4(2x + 7) = 36, apply the distributive property, create an equivalent equation by isolating the variable x, and then divide by the coefficient of x. Checking the solution by substituting the value of x back into the original equation confirms its correctness.
Step-by-step explanation:
To solve the multi-step equation 4(2x + 7) = 36, you first use the distributive property to remove the parenthesis. Multiply 4 by each term inside the parenthesis:
4 × 2x + 4 × 7 = 36
Which simplifies to:
8x + 28 = 36
Next, you want to create an equivalent equation by getting the variable x by itself on one side of the equation. Subtract 28 from both sides:
8x + 28 - 28 = 36 - 28
This gives us:
8x = 8
Now, divide both sides by 8, which is the coefficient of x, to isolate the variable:
8x ÷ 8 = 8 ÷ 8
Thus, we get:
x = 1
Finally, check the answer by substituting x back into the original equation to see if it is reasonable. Substituting x = 1 gives 4(2(1) + 7) which equals 4(2 + 7) = 4(9) = 36, confirming our solution is correct.