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Math  /  Algebra

Question16x+35=1−310x\frac{1}{6} x+\frac{3}{5}=1-\frac{3}{10} x

Studdy Solution

STEP 1

1. The equation involves fractions and requires finding a common denominator.
2. The goal is to solve for x x .
3. We will perform operations to isolate x x on one side of the equation.

STEP 2

1. Eliminate fractions by finding a common denominator.
2. Move all terms involving x x to one side of the equation.
3. Simplify and solve for x x .

STEP 3

Identify the least common denominator (LCD) for the fractions. The denominators are 6, 5, and 10. The LCD is 30.
Multiply every term by 30 to eliminate the fractions:
30(16x)+30(35)=30(1)−30(310x) 30 \left(\frac{1}{6} x\right) + 30 \left(\frac{3}{5}\right) = 30 \left(1\right) - 30 \left(\frac{3}{10} x\right)

STEP 4

Simplify each term:
5x+18=30−9x 5x + 18 = 30 - 9x

STEP 5

Move all terms involving x x to one side of the equation. Add 9x 9x to both sides:
5x+9x+18=30 5x + 9x + 18 = 30

STEP 6

Combine like terms:
14x+18=30 14x + 18 = 30

STEP 7

Isolate x x by subtracting 18 from both sides:
14x=12 14x = 12

STEP 8

Solve for x x by dividing both sides by 14:
x=1214 x = \frac{12}{14}
Simplify the fraction:
x=67 x = \frac{6}{7}
The solution is:
67 \boxed{\frac{6}{7}}

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