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Math  /  Algebra

QuestionGiven the equation x/3=−12x / 3=-12, the value of x=−4x=-4.
A True B False Find the value of xx if the answer is false: \qquad

Studdy Solution

STEP 1

1. We are given the equation x3=−12 \frac{x}{3} = -12 .
2. We need to determine if the statement x=−4 x = -4 is true or false.
3. If the statement is false, we need to find the correct value of x x .

STEP 2

1. Verify the given value of x x .
2. Solve the equation x3=−12 \frac{x}{3} = -12 for x x .
3. Determine if the given value is correct.
4. If false, provide the correct value of x x .

STEP 3

Verify the given value of x x by substituting x=−4 x = -4 into the equation:
−43=−43 \frac{-4}{3} = -\frac{4}{3}
Compare this with −12-12.

STEP 4

Solve the equation x3=−12 \frac{x}{3} = -12 for x x .
Multiply both sides by 3 to isolate x x :
x=−12×3 x = -12 \times 3

STEP 5

Calculate the right-hand side:
x=−36 x = -36

STEP 6

Determine if the given value x=−4 x = -4 is correct by comparing it to our solution x=−36 x = -36 .
Since −4≠−36-4 \neq -36, the given value is incorrect.

STEP 7

Since the statement is false, the correct value of x x is:
x=−36 x = -36
The answer is B: False. The correct value of x x is −36 \boxed{-36} .

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