Show all steps solve the equation 0.25r-0.125+0.5r=0.5+r

0.25r-0.125+0.5r=0.5+r

0.25r + 0.5r - 0.125 = 0.5 * r

0.75r - r = 0.125 + 0.5

-0.25r = 0.625

r = 0.625 / -0.25

r = -2.5

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Step 1: Distribute the 0.25 and 0.5 on the left side of the equation:

0.25r - 0.125 + 0.5r = 0.5 + r
(0.25r + 0.5r) - 0.125 = 0.5 + r

Step 2: Combine like terms on the left side of the equation:
0.75r - 0.125 = 0.5 + r

Step 3: Subtract r from both sides of the equation to isolate the r terms:
0.75r - 0.125 - r = 0.5 + r - r
0.75r - r - 0.125 = 0.5

Step 4: Combine like terms on the left side of the equation:
(0.75 - 1)r - 0.125 = 0.5
-0.25r - 0.125 = 0.5

Step 5: Add 0.125 to both sides of the equation to isolate the constant term:
-0.25r - 0.125 + 0.125 = 0.5 + 0.125
-0.25r = 0.625

Step 6: Divide both sides of the equation by -0.25 to solve for r:
-0.25r / -0.25 = 0.625 / -0.25
r = -2.5

Step 7: Check the solution by substituting the value of r back into the original equation:
0.25r - 0.125 + 0.5r = 0.5 + r
0.25(-2.5) - 0.125 + 0.5(-2.5) = 0.5 + (-2.5)
-0.625 - 0.125 - 1.25 = -2.5
-1.75 - 1.25 = -2.5
-3 = -2.5

The solution checks out, so the value of r is -2.5.

To solve the equation 0.25r - 0.125 + 0.5r = 0.5 + r, follow these steps:

Step 1: Combine like terms on both sides of the equation:
We have 0.25r + 0.5r - r = 0.5 + 0.125.

Simplifying further, we get: 0.75r = 0.625.

Step 2: Isolate the variable r:
To isolate r, we need to get rid of the coefficient (0.75) multiplying r. To do this, we divide both sides of the equation by 0.75:

(0.75r)/0.75 = 0.625/0.75.

Simplifying further, we get: r = 0.8333.

Therefore, the solution to the equation 0.25r - 0.125 + 0.5r = 0.5 + r is r = 0.8333.