Solve for x (x-12)÷6=12
In this problem, you are tasked with solving an algebraic equation to find the value of the variable "x". The equation presented is in the form of a simple linear equation where "x" is initially within a parenthetical expression, subtracted by the number 12 and then divided by 6. The result of this expression is set equal to 12. Your goal is to perform algebraic manipulations such as distributing, adding, subtracting, multiplying, or dividing both sides of the equation by appropriate constants to isolate "x" and find its numerical value.
$\left(\right. x - 12 \left.\right) \div 6 = 12$
Answer
Solution:
Step 1:
Apply the multiplication property of equality to eliminate the denominator by multiplying both sides by $6$.
$6 \times \frac{x - 12}{6} = 6 \times 12$
Step 2:
Perform simplification on both sides of the equation.
Step 2.1:
Simplify the left-hand side.
Step 2.1.1:
Remove the division by $6$ by multiplying.
Step 2.1.1.1:
Express the division as a multiplication by the reciprocal.
$6 \times \frac{x - 12}{6} = 6 \times 12$
Step 2.1.1.2:
Eliminate the common factors.
Step 2.1.1.2.1:
Reduce the fraction by cancelling out the $6$.
$\frac{6}{6}(x - 12) = 6 \times 12$
Step 2.1.1.2.2:
Simplify to get the linear expression.
$x - 12 = 6 \times 12$
Step 2.2:
Simplify the right-hand side.
Step 2.2.1:
Calculate the product of $6$ and $12$.
$x - 12 = 72$
Step 3:
Isolate the variable $x$ by moving constants to the other side.
Step 3.1:
Add $12$ to both sides to cancel the subtraction.
$x = 72 + 12$
Step 3.2:
Combine the constants to find the value of $x$.
$x = 84$
Knowledge Notes:
To solve the equation $(x-12)÷6=12$, we follow a systematic approach:
Multiplication Property of Equality: This property allows us to multiply both sides of an equation by the same nonzero number without changing the equality. This is used to clear fractions or decimals from an equation.
Simplification: This involves combining like terms and simplifying expressions on both sides of the equation. When dealing with fractions, we often look for common factors that can be cancelled out.
Isolating the Variable: The goal is to get the variable on one side of the equation and the constants on the other. This typically involves using addition or subtraction to move terms from one side to the other, and multiplication or division to get the variable by itself.
Combining Like Terms: When we have the same variable or constant on both sides of the equation, we combine them to simplify the equation further.
In this problem, we used these principles to first eliminate the fraction by multiplying both sides by $6$, then we simplified the resulting expression and isolated the variable $x$ to find its value.
