Solve (2-3x)/5<(1-x)/3<(34x)/2

Question

Solve the inequality

x > \frac{1}{4}

Alternative Form

x \in (\frac{1}{4}, + \infty)

Evaluate

\frac{2 - 3 x}{5} < \frac{1 - x}{3} < \frac{34 x}{2}

Separate into two inequalities

{\frac{2 - 3 x}{5} < \frac{1 - x}{3} \frac{1 - x}{3} < \frac{34 x}{2}

Solve the inequality

More Steps

Evaluate

\frac{2 - 3 x}{5} < \frac{1 - x}{3}

Cross multiply

(2 - 3 x) \times 3 < 5 (1 - x)

Simplify the equation

3 (2 - 3 x) < 5 (1 - x)

Calculate

More Steps

Evaluate

3 (2 - 3 x)

Apply the distributive property

3 \times 2 - 3 \times 3 x

Multiply the numbers

6 - 3 \times 3 x

Multiply the numbers

6 - 9 x

6 - 9 x = 5 (1 - x)

Calculate

More Steps

Evaluate

5 (1 - x)

Apply the distributive property

5 \times 1 - 5 x

Any expression multiplied by 1 remains the same

5 - 5 x

6 - 9 x = 5 - 5 x

Move the expression to the left side

6 - 9 x - (5 - 5 x) < 0

Calculate

More Steps

Add the terms

6 - 9 x - (5 - 5 x)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

6 - 9 x - 5 + 5 x

Subtract the numbers

1 - 9 x + 5 x

Add the terms

1 - 4 x

1 - 4 x < 0

Move the constant to the right side

- 4 x < 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

- 4 x < - 1

Change the signs on both sides of the inequality and flip the inequality sign

4 x > 1

Divide both sides

\frac{4 x}{4} > \frac{1}{4}

Divide the numbers

x > \frac{1}{4}

{x > \frac{1}{4} \frac{1 - x}{3} < \frac{34 x}{2}

Solve the inequality

More Steps

Evaluate

\frac{1 - x}{3} < \frac{34 x}{2}

Divide the terms

More Steps

Evaluate

\frac{34}{2}

Reduce the numbers

\frac{17}{1}

Calculate

17

\frac{1 - x}{3} < 17 x

Cross multiply

1 - x < 3 \times 17 x

Simplify the equation

1 - x < 51 x

Move the variable to the left side

1 - x - 51 x < 0

Subtract the terms

More Steps

Evaluate

- x - 51 x

Collect like terms by calculating the sum or difference of their coefficients

(- 1 - 51) x

Subtract the numbers

- 52 x

1 - 52 x < 0

Move the constant to the right side

- 52 x < 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

- 52 x < - 1

Change the signs on both sides of the inequality and flip the inequality sign

52 x > 1

Divide both sides

\frac{52 x}{52} > \frac{1}{52}

Divide the numbers

x > \frac{1}{52}

{x > \frac{1}{4} x > \frac{1}{52}

Solution

x > \frac{1}{4}

Alternative Form

x \in (\frac{1}{4}, + \infty)

Show Solution