Solve |x-1|-|2x-5|=10 - ScanMath

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Type your math problem... |x-1|-|2x-5|=10

Question

Solve the equation

x \in \emptyset

Alternative Form

No solution

Evaluate

∣ x - 1 ∣ - ∣ 2 x - 5 ∣ = 10

Move the expression to the left side

∣ x - 1 ∣ - ∣ 2 x - 5 ∣ - 10 = 0

Separate the equation into 4 possible cases

x - 1 - (2 x - 5) - 10 = 0, x - 1 \geq 0, 2 x - 5 \geq 0 x - 1 - (- (2 x - 5)) - 10 = 0, x - 1 \geq 0, 2 x - 5 < 0 - (x - 1) - (2 x - 5) - 10 = 0, x - 1 < 0, 2 x - 5 \geq 0 - (x - 1) - (- (2 x - 5)) - 10 = 0, x - 1 < 0, 2 x - 5 < 0

Solve the equation

More Steps

x = - 6, x - 1 \geq 0, 2 x - 5 \geq 0 x - 1 - (- (2 x - 5)) - 10 = 0, x - 1 \geq 0, 2 x - 5 < 0 - (x - 1) - (2 x - 5) - 10 = 0, x - 1 < 0, 2 x - 5 \geq 0 - (x - 1) - (- (2 x - 5)) - 10 = 0, x - 1 < 0, 2 x - 5 < 0

Solve the inequality

More Steps

x = - 6, x \geq 1, 2 x - 5 \geq 0 x - 1 - (- (2 x - 5)) - 10 = 0, x - 1 \geq 0, 2 x - 5 < 0 - (x - 1) - (2 x - 5) - 10 = 0, x - 1 < 0, 2 x - 5 \geq 0 - (x - 1) - (- (2 x - 5)) - 10 = 0, x - 1 < 0, 2 x - 5 < 0

Solve the inequality

More Steps

x = - 6, x \geq 1, x \geq \frac{5}{2} x - 1 - (- (2 x - 5)) - 10 = 0, x - 1 \geq 0, 2 x - 5 < 0 - (x - 1) - (2 x - 5) - 10 = 0, x - 1 < 0, 2 x - 5 \geq 0 - (x - 1) - (- (2 x - 5)) - 10 = 0, x - 1 < 0, 2 x - 5 < 0

Solve the equation

More Steps

x = - 6, x \geq 1, x \geq \frac{5}{2} x = \frac{16}{3}, x - 1 \geq 0, 2 x - 5 < 0 - (x - 1) - (2 x - 5) - 10 = 0, x - 1 < 0, 2 x - 5 \geq 0 - (x - 1) - (- (2 x - 5)) - 10 = 0, x - 1 < 0, 2 x - 5 < 0

Solve the inequality

More Steps

x = - 6, x \geq 1, x \geq \frac{5}{2} x = \frac{16}{3}, x \geq 1, 2 x - 5 < 0 - (x - 1) - (2 x - 5) - 10 = 0, x - 1 < 0, 2 x - 5 \geq 0 - (x - 1) - (- (2 x - 5)) - 10 = 0, x - 1 < 0, 2 x - 5 < 0

Solve the inequality

More Steps

x = - 6, x \geq 1, x \geq \frac{5}{2} x = \frac{16}{3}, x \geq 1, x < \frac{5}{2} - (x - 1) - (2 x - 5) - 10 = 0, x - 1 < 0, 2 x - 5 \geq 0 - (x - 1) - (- (2 x - 5)) - 10 = 0, x - 1 < 0, 2 x - 5 < 0

Solve the equation

More Steps

x = - 6, x \geq 1, x \geq \frac{5}{2} x = \frac{16}{3}, x \geq 1, x < \frac{5}{2} x = - \frac{4}{3}, x - 1 < 0, 2 x - 5 \geq 0 - (x - 1) - (- (2 x - 5)) - 10 = 0, x - 1 < 0, 2 x - 5 < 0

Solve the inequality

More Steps

x = - 6, x \geq 1, x \geq \frac{5}{2} x = \frac{16}{3}, x \geq 1, x < \frac{5}{2} x = - \frac{4}{3}, x < 1, 2 x - 5 \geq 0 - (x - 1) - (- (2 x - 5)) - 10 = 0, x - 1 < 0, 2 x - 5 < 0

Solve the inequality

More Steps

x = - 6, x \geq 1, x \geq \frac{5}{2} x = \frac{16}{3}, x \geq 1, x < \frac{5}{2} x = - \frac{4}{3}, x < 1, x \geq \frac{5}{2} - (x - 1) - (- (2 x - 5)) - 10 = 0, x - 1 < 0, 2 x - 5 < 0

Solve the equation

More Steps

x = - 6, x \geq 1, x \geq \frac{5}{2} x = \frac{16}{3}, x \geq 1, x < \frac{5}{2} x = - \frac{4}{3}, x < 1, x \geq \frac{5}{2} x = 14, x - 1 < 0, 2 x - 5 < 0

Solve the inequality

More Steps

x = - 6, x \geq 1, x \geq \frac{5}{2} x = \frac{16}{3}, x \geq 1, x < \frac{5}{2} x = - \frac{4}{3}, x < 1, x \geq \frac{5}{2} x = 14, x < 1, 2 x - 5 < 0

Solve the inequality

More Steps

x = - 6, x \geq 1, x \geq \frac{5}{2} x = \frac{16}{3}, x \geq 1, x < \frac{5}{2} x = - \frac{4}{3}, x < 1, x \geq \frac{5}{2} x = 14, x < 1, x < \frac{5}{2}

Find the intersection

x \in \emptyset x = \frac{16}{3}, x \geq 1, x < \frac{5}{2} x = - \frac{4}{3}, x < 1, x \geq \frac{5}{2} x = 14, x < 1, x < \frac{5}{2}

Find the intersection

x \in \emptyset x \in \emptyset x = - \frac{4}{3}, x < 1, x \geq \frac{5}{2} x = 14, x < 1, x < \frac{5}{2}

Find the intersection

x \in \emptyset x \in \emptyset x \in \emptyset x = 14, x < 1, x < \frac{5}{2}

Find the intersection

x \in \emptyset x \in \emptyset x \in \emptyset x \in \emptyset

Solution

x \in \emptyset

Alternative Form

No solution

Show Solution

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