To solve the equation: 24(34+x)=1,200
, give the reasons for each of the given steps.
Step 1: 816+24x=1,200
Step 2: 816−816+24x=1,200 − 816
Step 3: 24x=384
Step 4: x=16
Step 1: Distributive Property - Multiply 24 by (34+x) to get 816+24x on the left side of the equation.
Step 2: Simplification - Subtract 816 from both sides of the equation to isolate the variable term (24x) on the left side. Subtract 816 from 1,200 to get 384 on the right side.
Step 3: Simplification - Combine like terms on the left side to have only 24x. 816-816 is 0, so it is eliminated from the equation.
Step 4: Isolation of variable - Divide both sides of the equation by 24 to solve for x. The 24 on the left side cancels out, leaving only x. Divide 384 by 24 to get 16 on the right side.
can you awnser with the following options?
multiplication as the inverse operation to isolate the variable
distributive property
subtraction as the inverse operation to isolate the variable
combine like terms
addition as the inverse operation to isolate the variable
division as the inverse operation to isolate the variable
Step 1: Distributive Property - This step involves multiplying 24 by (34+x) to get 816+24x on the left side of the equation.
Step 2: Subtraction as the inverse operation to isolate the variable - By subtracting 816 from both sides, we can isolate the variable term (24x) on the left side, making the equation 816+24x - 816 = 1,200 - 816.
Step 3: Combine like terms - This step involves simplifying the equation by combining like terms on the left side of the equation. 816 - 816 is 0, so it is eliminated from the equation.
Step 4: Division as the inverse operation to isolate the variable - By dividing both sides of the equation by 24, we can solve for x. The 24 on the left side cancels out, leaving only x. Dividing 384 by 24 gives us 16 on the right side. Therefore, x = 16.
Step 1: To solve the equation, we distribute the 24 to both the terms inside the parentheses: 24 * 34 + 24 * x = 1,200. This simplifies to 816 + 24x = 1,200.
Step 2: Next, we subtract 816 from both sides of the equation to isolate the term with x: 816 - 816 + 24x = 1,200 - 816. This simplifies to 24x = 384.
Step 3: Now, we have a simple linear equation with one variable, x. In order to solve for x, we divide both sides of the equation by 24: 24x / 24 = 384 / 24. This simplifies to x = 16.
Step 4: Therefore, the solution to the equation 24(34 + x) = 1,200 is x = 16.