Solve the proportion for x. round your answer to two decimal places.
2x/x+10=0.04/1.85
2x/(x+10)=0.04/1.85
2x*1.85=(x+10)*0.04
3.7x=0.04x+0.4
3.7x-0.04x=0.4
3.66x=0.4
x=0.4/3.66
x=0.10928961748633879781420765027322
To solve the proportion (equation) for x, we need to isolate x on one side of the equation.
Step 1: Multiply both sides of the equation by (x + 10) to eliminate the fraction on the left side:
2x(x + 10) / (x + 10) = (0.04 / 1.85)(x + 10)
Simplifying:
2x = (0.04 / 1.85)(x + 10)
Step 2: Distribute the right side of the equation:
2x = (0.04 / 1.85)x + (0.04 / 1.85)(10)
Simplifying:
2x = (0.04x / 1.85) + (0.04 * 10 / 1.85)
Step 3: Bring all the terms with x to one side by subtracting (0.04x / 1.85) from both sides:
2x - (0.04x / 1.85) = (0.04 * 10 / 1.85)
Combining like terms:
(2 - 0.04 / 1.85)x = (0.04 * 10 / 1.85)
Simplifying:
(1.96 / 1.85)x = (0.04 * 10 / 1.85)
Step 4: Solve for x by dividing both sides of the equation by (1.96 / 1.85):
x = (0.04 * 10 / 1.85) / (1.96 / 1.85)
Simplifying:
x = (0.4 / 1.85) / (1.96 / 1.85)
Dividing:
x = 0.2162162 (rounded to two decimal places)
Therefore, the value of x in the proportion 2x / (x + 10) = 0.04 / 1.85 is approximately 0.22 (rounded to two decimal places).