Solve |2x-7| 1=9|2x-7| 1=9

Question

Solve the system of equations

x \in \emptyset

Alternative Form

No solution

Evaluate

{∣ 2 x - 7 ∣ \times 1 = 9 ∣ 2 x - 7 ∣ \times 1 9 ∣ 2 x - 7 ∣ \times 1 = 9

Calculate

More Steps

Evaluate

∣ 2 x - 7 ∣ \times 1 = 9 ∣ 2 x - 7 ∣ \times 1

Any expression multiplied by 1 remains the same

∣ 2 x - 7 ∣ = 9 ∣ 2 x - 7 ∣ \times 1

Multiply the terms

∣ 2 x - 7 ∣ = 9 ∣ 2 x - 7 ∣

Move the expression to the left side

∣ 2 x - 7 ∣ - 9 ∣ 2 x - 7 ∣ = 0

Subtract the terms

More Steps

Evaluate

∣ 2 x - 7 ∣ - 9 ∣ 2 x - 7 ∣

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

(1 - 9) ∣ 2 x - 7 ∣

Subtract the numbers

- 8 ∣ 2 x - 7 ∣

- 8 ∣ 2 x - 7 ∣ = 0

Change the sign

8 ∣ 2 x - 7 ∣ = 0

Rewrite the expression

∣ 2 x - 7 ∣ = 0

Rewrite the expression

2 x - 7 = 0

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

2 x = 0 + 7

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

2 x = 7

Divide both sides

\frac{2 x}{2} = \frac{7}{2}

Divide the numbers

x = \frac{7}{2}

{x = \frac{7}{2} 9 ∣ 2 x - 7 ∣ \times 1 = 9

Calculate

More Steps

Evaluate

9 ∣ 2 x - 7 ∣ \times 1 = 9

Multiply the terms

9 ∣ 2 x - 7 ∣ = 9

Divide both sides

\frac{9 ∣ 2 x - 7 ∣}{9} = \frac{9}{9}

Divide the numbers

∣ 2 x - 7 ∣ = \frac{9}{9}

Divide the numbers

More Steps

Evaluate

\frac{9}{9}

Reduce the numbers

\frac{1}{1}

Calculate

1

∣ 2 x - 7 ∣ = 1

Separate the equation into 2 possible cases

2 x - 7 = 1 \cup 2 x - 7 = - 1

Solve the equation for x

More Steps

Evaluate

2 x - 7 = 1

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

2 x = 1 + 7

Add the numbers

2 x = 8

Divide both sides

\frac{2 x}{2} = \frac{8}{2}

Divide the numbers

x = \frac{8}{2}

Divide the numbers

x = 4

x = 4 \cup 2 x - 7 = - 1

Solve the equation for x

More Steps

Evaluate

2 x - 7 = - 1

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

2 x = - 1 + 7

Add the numbers

2 x = 6

Divide both sides

\frac{2 x}{2} = \frac{6}{2}

Divide the numbers

x = \frac{6}{2}

Divide the numbers

x = 3

x = 4 \cup x = 3

{x = \frac{7}{2} x = 4 \cup x = 3

Solution

x \in \emptyset

Alternative Form

No solution

Show Solution