Math  /  Algebra

QuestionSolve for uu. 12u67=45-\frac{1}{2} u-\frac{6}{7}=-\frac{4}{5}
Simplify your answer as much as possible.

Studdy Solution

STEP 1

1. The problem involves a linear equation with one variable, uu.
2. The equation can be solved by isolating uu on one side of the equation.
3. Basic algebraic operations such as addition, subtraction, multiplication, and division will be used to solve the equation.
4. The final answer should be simplified to its simplest form.

STEP 2

1. Eliminate the fractions by finding a common denominator and multiplying both sides of the equation by it.
2. Simplify the equation by combining like terms and isolating the variable uu.
3. Solve for uu.
4. Simplify the solution, if necessary.

STEP 3

Identify the common denominator for the fractions involved, which are 12\frac{1}{2}, 67\frac{6}{7}, and 45\frac{4}{5}. The least common multiple (LCM) of 22, 77, and 55 is 7070.

STEP 4

Multiply both sides of the equation by 7070 to eliminate the fractions.
70(12u67)=70(45) 70 \left(-\frac{1}{2} u - \frac{6}{7}\right) = 70 \left(-\frac{4}{5}\right)

STEP 5

Distribute 7070 across the terms inside the parentheses.
7012u7067=7045 70 \cdot -\frac{1}{2} u - 70 \cdot \frac{6}{7} = 70 \cdot -\frac{4}{5}

STEP 6

Simplify each term by performing the multiplications.
35u60=56 -35u - 60 = -56

STEP 7

Add 6060 to both sides of the equation to start isolating uu.
35u60+60=56+60 -35u - 60 + 60 = -56 + 60

STEP 8

Simplify both sides.
35u=4 -35u = 4

STEP 9

Divide both sides by 35-35 to solve for uu.
u=435 u = \frac{4}{-35}

STEP 10

Simplify the fraction.
u=435 u = -\frac{4}{35}
Solution: u=435 u = -\frac{4}{35}

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