Give me another example of this question: multiple choice which equation is equivalent to 3(x-4)=45.

Understand the Problem

The question is asking for a different example of a multiple-choice question that involves finding an equivalent equation to a given equation, specifically 3(x-4)=45.

Answer

$3(15) = 45$

Steps to Solve

Identify the given equation

The equation we have is $3(x - 4) = 45$.

Distribute the coefficient

Distribute the 3 on the left side of the equation:

$$ 3(x - 4) = 3x - 12 $$

So, the equation becomes:

$$ 3x - 12 = 45 $$

Isolate the variable

Next, we want to isolate $x$ by adding 12 to both sides:

$$ 3x - 12 + 12 = 45 + 12 $$

This simplifies to:

$$ 3x = 57 $$

Solve for $x$

Divide both sides by 3 to find $x$:

$$ x = \frac{57}{3} $$

This simplifies to:

$$ x = 19 $$

Formulate an equivalent equation

Now, an equivalent equation could be found by substituting $x = 19$ back into the original format of the equation.

If we replace $x$ with 19, we have:

$$ 3(19 - 4) = 45 $$

Thus, another example of an equivalent equation is:

$$ 3(15) = 45 $$

An equivalent equation is $3(15) = 45$.

More Information

This alternative equation maintains the same relationship as the original equation while showcasing different numerical values. It's useful for understanding equivalence in algebraic expressions.

Tips

A common mistake is to forget to distribute properly, which can lead to incorrect equivalent expressions. Always double-check the distribution step.
Another error can occur when isolating the variable, such as forgetting to balance the equation by adding or subtracting the same number from both sides.

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