To solve the equation: 24(34+x)=1,200
, give the reasons for each of the given steps.
What was done to the previous step to get to the current equation?
(1 point)
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Step 1: 816+24x=1,200
Step 2: 816−816+24x=1,200 − 816
Step 3: 24x=384
Step 4: x=16
Step 1: 816+24x=1,200
Reason: We distributed the 24 to both terms inside the parentheses.
Step 2: 816−816+24x=1,200−816
Reason: We subtracted 816 from both sides to isolate the term with x on one side of the equation.
Step 3: 24x=384
Reason: We simplified the equation by combining like terms on the left side of the equation.
Step 4: x=16
Reason: We divided both sides of the equation by 24 to solve for x.
Simplify: −4(2x+5)
To solve the equation: 24(34+x)=1,200, the following steps were taken:
Step 1: Distribute 24 to both terms inside the parentheses, resulting in 816 + 24x = 1,200.
Reason: The distributive property states that multiplying a number by a sum is the same as multiplying the number by each term in the sum and then adding the products.
Step 2: Subtract 816 from both sides of the equation, giving 816 - 816 + 24x = 1,200 - 816.
Reason: To isolate the variable term, we need to eliminate the constant term on the same side. By subtracting 816 from both sides, we cancel out the 816 on the left side, leaving only 24x.
Step 3: Simplify the equation by combining like terms, resulting in 24x = 384.
Reason: This step combines the terms -816 and 1,200 - 816 to simplify the equation.
Step 4: Divide both sides of the equation by 24, giving x = 16.
Reason: To solve for x, we need to isolate it on one side of the equation. By dividing both sides by 24, we cancel out the 24 on the left side, leaving only x.
To solve the equation 24(34+x) = 1,200, the following steps were taken:
Step 1: Distribute the 24 to both terms inside the parentheses
Reason: This step is done to remove the parentheses and simplify the equation.
Result: 816 + 24x = 1,200
Step 2: Subtract 816 from both sides of the equation
Reason: This step is done to isolate the term with the variable on one side of the equation.
Result: 816 - 816 + 24x = 1,200 - 816
24x = 384
Step 3: Simplify the equation by performing the subtraction on the left side and the subtraction on the right side.
Reason: This step further simplifies the equation to get it into a form where x can be easily solved for.
Result: 24x = 384
Step 4: Divide both sides of the equation by 24
Reason: This step is done to isolate x and solve for its value.
Result: x = 16
Therefore, the value of x that solves the equation is 16.