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Math  /  Algebra

QuestionThe graph of y=−45x−1y=-\frac{4}{5} x-1 is shown below. Use the dot tool to plot the point on the graph that shows the solution to −45x−1=7-\frac{4}{5} x-1=7
Clear All Draw:
What is the solution? x=x= □\square

Studdy Solution

STEP 1

1. The equation −45x−1=7 -\frac{4}{5}x - 1 = 7 is a linear equation.
2. We are tasked with finding the value of x x that satisfies this equation.
3. The solution involves basic algebraic operations, specifically addition and division.

STEP 2

1. Isolate the linear expression.
2. Solve for x x .
3. Verify the solution by substituting back into the equation.

STEP 3

Start by isolating the term with x x on one side of the equation. Add 1 to both sides to eliminate the constant term on the left:
−45x−1+1=7+1 -\frac{4}{5}x - 1 + 1 = 7 + 1
This simplifies to:
−45x=8 -\frac{4}{5}x = 8

STEP 4

Now, solve for x x by dividing both sides by −45-\frac{4}{5}. This is the same as multiplying by the reciprocal:
x=8−45 x = \frac{8}{-\frac{4}{5}}
Simplify the right side:
x=8×−54 x = 8 \times -\frac{5}{4}
x=−10 x = -10

STEP 5

Verify the solution by substituting x=−10 x = -10 back into the original equation:
−45(−10)−1=7 -\frac{4}{5}(-10) - 1 = 7
Calculate the left side:
405−1=7 \frac{40}{5} - 1 = 7
8−1=7 8 - 1 = 7
7=7 7 = 7
The left side equals the right side, confirming our solution is correct.
The solution is:
x=−10 x = \boxed{-10}

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