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: Multiply 24 by (34+x) on the left side of the equation to obtain the expression 24(34+x).
Step 2: Simplify the left side of the equation by subtracting 816 from both sides. This is done in order to isolate the variable x on one side of the equation.
Step 3: Simplify the left side of the equation by combining like terms.
Step 4: Divide both sides of the equation by 24 to solve for the variable x.
bot the answer choices are 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, multiplication as the inverse operation to isolate the variable.
Step 1: Distributive property, as the expression 24(34+x) is multiplied out.
Step 2: Subtraction as the inverse operation to isolate the variable. Subtracting 816 from both sides moves the constant term to the other side of the equation.
Step 3: Combining like terms, as 816 - 816 simplifies to 0 on the left side of the equation.
Step 4: Division as the inverse operation to isolate the variable. The variable x is divided by 24 on both sides to solve for its value.
The number of x's on both sides of the equation is different a≠b
How many solutions does this equation have?
To solve the equation 24(34+x) = 1200, the following steps were performed:
Step 1: Distributive property. The equation is multiplied by 24 on the left side: 24 * 34 + 24 * x = 1200. This results in 816 + 24x = 1200.
Step 2: Combining like terms. The constant term 816 is subtracted from both sides of the equation to isolate the term with the variable: 816 - 816 + 24x = 1200 - 816. This simplifies to 24x = 384.
Step 3: Isolating the variable. The equation is divided by 24 on both sides to solve for x: 24x / 24 = 384 / 24. This simplifies to x = 16.
Therefore, x=16 is the solution to the equation.
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. This gives us 816 + 24x = 1,200. The reason for this step is the distributive property of multiplication over addition.
Step 2: To isolate the term with the variable (24x), we can get rid of the constant term (816) on the left side by subtracting it from both sides of the equation. This results in 816 - 816 + 24x = 1,200 - 816. The reason for this step is to simplify the equation by eliminating the constant term on the left side.
Step 3: After simplifying the equation from step 2, we get 24x = 384. The reason for this step is to combine like terms and simplify the equation further.
Step 4: To solve for x, we divide both sides of the equation by the coefficient of x, which is 24. This gives us x = 16. The reason for this step is to isolate the variable x and find its value.