Final answer:
The equation 3(x − 4) = 12x is solved through algebraic rearrangement, distributing the 3, getting terms with x on one side, and finally dividing by the coefficient of x to find that the solution is x = -4/3.
Step-by-step explanation:
The student's question involves solving the equation 3(x − 4) = 12x. To solve this equation, we need to use algebraic rearrangement techniques. Here's the step-by-step process:
- Distribute the 3 to both terms inside the parentheses: 3 * x - 3 * 4 = 12x, which simplifies to 3x - 12 = 12x.
- Next, we want to get all terms with x on one side of the equation, so we subtract 3x from both sides: 3x - 12 - 3x = 12x - 3x, resulting in -12 = 9x.
- To isolate x, we divide both sides by 9: -12 / 9 = 9x / 9. Simplifying this gives us x = -4/3 or approximately x = -1.33.
Therefore, the solution to the equation 3(x − 4) = 12x is x = -4/3.
In the equation
x=5y+4z, the variable x
is the subject of the equation. This means it is expressed in terms of the other variables. To rearrange an equation so that another variable becomes the subject, perform the same operations on both sides of the equals sign so that eventually this variable is by itself on the left hand side. Performing the same operations on both sides makes sure that the left hand side is always equal to the right hand side. Operations which we can use include:
- Adding or subtracting a quantity
- Multiplying or dividing by a quantity
- Raising to any power (except the power zero)
- Taking logarithms or exponentiating
Note: We don't raise both sides of an equation to the power of zero because anything raised the power of zero is equal to 1 and so this would give us 1=1.