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Math  /  Algebra

Question6=−43u6=-\frac{4}{3} u

Studdy Solution

STEP 1

1. The equation 6=−43u 6 = -\frac{4}{3} u is asking us to solve for u u .
2. This is a one-step equation involving a fraction.
3. The equation involves basic algebraic operations, specifically multiplication and division.

STEP 2

1. Understand the structure of the equation.
2. Isolate the variable u u by performing algebraic operations.
3. Check the solution by substituting it back into the original equation.

STEP 3

The equation 6=−43u 6 = -\frac{4}{3} u indicates that 6 6 is equal to −43-\frac{4}{3} times u u .

STEP 4

To isolate u u , multiply both sides of the equation by the reciprocal of −43-\frac{4}{3}, which is −34-\frac{3}{4}:
6×(−34)=u 6 \times \left(-\frac{3}{4}\right) = u

STEP 5

Calculate the left-hand side:
6×(−34)=−184=−92 6 \times \left(-\frac{3}{4}\right) = -\frac{18}{4} = -\frac{9}{2}
Thus, u=−92 u = -\frac{9}{2} .

STEP 6

Check the solution by substituting u=−92 u = -\frac{9}{2} back into the original equation:
6=−43(−92) 6 = -\frac{4}{3} \left(-\frac{9}{2}\right)

STEP 7

Simplify the right-hand side:
−43×−92=366=6 -\frac{4}{3} \times -\frac{9}{2} = \frac{36}{6} = 6
Both sides of the equation are equal, confirming the solution is correct.
The solution is:
−92 \boxed{-\frac{9}{2}}

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