Solve 5n-3=|n 9| - ScanMath

Question

Solve the equation

n \in \emptyset

Alternative Form

No solution

Evaluate

5 n - 3 = ∣ n \times 9 ∣

Use the commutative property to reorder the terms

5 n - 3 = ∣ 9 n ∣

Swap the sides

∣ 9 n ∣ = 5 n - 3

Rewrite the expression

∣ 9 n ∣ - 5 n + 3 = 0

Separate the equation into 2 possible cases

9 n - 5 n + 3 = 0, 9 n \geq 0 - 9 n - 5 n + 3 = 0, 9 n < 0

Solve the equation

More Steps

Evaluate

9 n - 5 n + 3 = 0

Calculate

More Steps

Evaluate

9 n - 5 n

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

(9 - 5) n

Subtract the numbers

4 n

4 n + 3 = 0

Move the constant to the right-hand side and change its sign

4 n = 0 - 3

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

4 n = - 3

Divide both sides

\frac{4 n}{4} = \frac{- 3}{4}

Divide the numbers

n = \frac{- 3}{4}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

n = - \frac{3}{4}

n = - \frac{3}{4}, 9 n \geq 0 - 9 n - 5 n + 3 = 0, 9 n < 0

Solve the inequality

n = - \frac{3}{4}, n \geq 0 - 9 n - 5 n + 3 = 0, 9 n < 0

Solve the equation

More Steps

Evaluate

- 9 n - 5 n + 3 = 0

Calculate

More Steps

Evaluate

- 9 n - 5 n

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

(- 9 - 5) n

Subtract the numbers

- 14 n

- 14 n + 3 = 0

Move the constant to the right-hand side and change its sign

- 14 n = 0 - 3

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

- 14 n = - 3

Change the signs on both sides of the equation

14 n = 3

Divide both sides

\frac{14 n}{14} = \frac{3}{14}

Divide the numbers

n = \frac{3}{14}

n = - \frac{3}{4}, n \geq 0 n = \frac{3}{14}, 9 n < 0

Solve the inequality

n = - \frac{3}{4}, n \geq 0 n = \frac{3}{14}, n < 0

Find the intersection

n \in \emptyset n = \frac{3}{14}, n < 0

Find the intersection

n \in \emptyset n \in \emptyset

Solution

n \in \emptyset

Alternative Form

No solution

Show Solution