QuestionSolve the equation: $0.25 r - 0.125 + 0.5 r = 0.5 + r$ . Show all steps.

Studdy Solution

STEP 1

Assumptions1. The equation to solve is $0.25 r-0.125+0.5 r=0.5+r$ . We are solving for the variable $r$

STEP 2

First, we need to simplify the equation by combining like terms on both sides of the equation. On the left side, we can combine $0.25r$ and $0.5r$ .
$0.25 r +0.5 r -0.125 =0.5 + r$

STEP 3

Calculate the sum of $0.25r$ and $0.5r$ on the left side of the equation.
$0.75 r -0.125 =0.5 + r$

STEP 4

Next, we need to isolate $r$ on one side of the equation. We can do this by subtracting $r$ from both sides of the equation.
$0.75 r - r -0.125 =0. + r - r$

STEP 5

Calculate the difference of $0.75r$ and $r$ on the left side of the equation.
$-0.25 r -0.125 =0.5$

STEP 6

Next, we need to isolate $r$ by adding $0.125$ to both sides of the equation.
$-0.25 r -0.125 +0.125 =0.5 +0.125$

STEP 7

Calculate the sum on the right side of the equation.
$-0.25 r =0.625$

STEP 8

Finally, we can solve for $r$ by dividing both sides of the equation by $-0.25$ .
$r = \frac{0.625}{-0.25}$

STEP 9

Calculate the value of $r$ .
$r = -2.5$ So, the solution to the equation is $r = -2.5$ .

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