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Half of $6$ time a number is $12$ decreased by the product of $3$ and the number

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Solve percent equations

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Q. Half of

6

time a number is

12

decreased by the product of

3

and the number

Define Number: Let's call the number we're looking for ＂x＂. The problem says half of $6$ times a number, so we write that as $(6 \times x) / 2$ .
Translate Problem: It also says this is equal to $12$ decreased by the product of $3$ and the number, which is $12 - 3 \times x$ .
Set Up Equation: Now we set up the equation: $(6 \times x) / 2 = 12 - 3 \times x$ .
Eliminate Fraction: To solve for $x$ , we first get rid of the fraction by multiplying both sides by $2$ : $2 \times \left(\frac{6 \times x}{2}\right) = 2 \times (12 - 3 \times x)$ .
Combine Like Terms: This simplifies to $6 \times x = 24 - 6 \times x$ .
Isolate Variable: Now, we add $6 \times x$ to both sides to get all the $x$ terms on one side: $6 \times x + 6 \times x = 24$ .
Solve for x: This gives us $12 \times x = 24$ .
Final Result: Finally, we divide both sides by $12$ to solve for x: $x = \frac{24}{12}$ .
Final Result: Finally, we divide both sides by $12$ to solve for x: $x = \frac{24}{12}$ .So, $x = 2$ . That's our number.

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