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Math  /  Algebra

QuestionSolve the equation 13d+8=−113 d+8=-1 d=d=

Studdy Solution

STEP 1

1. The equation 13d+8=−113d + 8 = -1 is a linear equation with one variable, dd.
2. We need to isolate dd to solve the equation.
3. The solution will be a single real number.

STEP 2

1. Simplify the equation by moving constants to one side.
2. Isolate the variable dd.
3. Check the solution.

STEP 3

First, we need to move the constant term 8 to the right side of the equation. We do this by subtracting 8 from both sides:
13d+8−8=−1−813d + 8 - 8 = -1 - 8
Simplifying, we get:
13d=−913d = -9

STEP 4

Now that we have isolated the term with dd on the left side, we need to divide both sides by 13 to isolate dd:
13d13=−913\frac{13d}{13} = \frac{-9}{13}
Simplifying, we get:
d=−913d = -\frac{9}{13}

STEP 5

Let's check our solution by substituting d=−913d = -\frac{9}{13} back into the original equation:
13(−913)+8=−113(-\frac{9}{13}) + 8 = -1
Simplifying the left side: −9+8=−1-9 + 8 = -1 −1=−1-1 = -1
The equation is true, so our solution is correct.
Therefore, the solution is:
d=−913d = -\frac{9}{13}

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