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Math  /  Algebra

Question斉. How many solutions does this equation have? 20−3u=−7u−17−1920-3 u=-7 u-17-19 [㮁] no solution one solution infinitely many solutions Submit

Studdy Solution

STEP 1

1. We are given a linear equation 20−3u=−7u−17−19 20 - 3u = -7u - 17 - 19 .
2. The goal is to determine the number of solutions to this equation.
3. A linear equation can have no solution, one solution, or infinitely many solutions.

STEP 2

1. Simplify the equation.
2. Collect like terms.
3. Solve for the variable u u .
4. Determine the number of solutions.

STEP 3

Simplify the right side of the equation:
−7u−17−19 -7u - 17 - 19
Combine the constants:
−17−19=−36 -17 - 19 = -36
Thus, the equation becomes:
20−3u=−7u−36 20 - 3u = -7u - 36

STEP 4

Collect like terms by moving all terms involving u u to one side and constant terms to the other side:
Add 7u 7u to both sides:
20−3u+7u=−36 20 - 3u + 7u = -36
This simplifies to:
20+4u=−36 20 + 4u = -36

STEP 5

Solve for u u by isolating it on one side of the equation:
Subtract 20 from both sides:
4u=−36−20 4u = -36 - 20
Simplify the right side:
4u=−56 4u = -56
Divide both sides by 4:
u=−14 u = -14

STEP 6

Since we found a specific value for u u , the equation has one solution.
The equation has one solution\boxed{\text{one solution}}.

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