Solve for x |3x-4|=|3x-5|

$| 3 x - 4 | = | 3 x - 5 |$

Step 1

Rewrite the equation as $| 3 x - 5 | = | 3 x - 4 |$ .

$| 3 x - 5 | = | 3 x - 4 |$

Step 2

Rewrite the absolute value equation as four equations without absolute value bars.

$3 x - 5 = 3 x - 4$

$3 x - 5 = - (3 x - 4)$

$- (3 x - 5) = 3 x - 4$

$- (3 x - 5) = - (3 x - 4)$

Step 3

After simplifying, there are only two unique equations to be solved.

$3 x - 5 = 3 x - 4$

$3 x - 5 = - (3 x - 4)$

Step 4

Solve $3 x - 5 = 3 x - 4$ for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $3 x$ from both sides of the equation.

$3 x - 5 - 3 x = - 4$

Combine the opposite terms in $3 x - 5 - 3 x$ .

Subtract $3 x$ from $3 x$ .

$0 - 5 = - 4$

Subtract $5$ from $0$ .

$- 5 = - 4$

Since $- 5 \neq - 4$ , there are no solutions.

No solution

Step 5

Solve $3 x - 5 = - (3 x - 4)$ for $x$ .

Simplify $- (3 x - 4)$ .

Rewrite.

$3 x - 5 = 0 + 0 - (3 x - 4)$

Simplify by adding zeros.

$3 x - 5 = - (3 x - 4)$

Apply the distributive property.

$3 x - 5 = - (3 x) - - 4$

Multiply.

Multiply $3$ by $- 1$ .

$3 x - 5 = - 3 x - - 4$

Multiply $- 1$ by $- 4$ .

$3 x - 5 = - 3 x + 4$

Move all terms containing $x$ to the left side of the equation.

Add $3 x$ to both sides of the equation.

$3 x - 5 + 3 x = 4$

Add $3 x$ and $3 x$ .

$6 x - 5 = 4$

Move all terms not containing $x$ to the right side of the equation.

Add $5$ to both sides of the equation.

$6 x = 4 + 5$

Add $4$ and $5$ .

$6 x = 9$

Divide each term in $6 x = 9$ by $6$ and simplify.

Divide each term in $6 x = 9$ by $6$ .

$\frac{6 x}{6} = \frac{9}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{9}{6}$

Divide $x$ by $1$ .

$x = \frac{9}{6}$

Simplify the right side.

Cancel the common factor of $9$ and $6$ .

Factor $3$ out of $9$ .

$x = \frac{3 (3)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$x = \frac{3 \cdot 3}{3 \cdot 2}$

Cancel the common factor.

$x = \frac{3 \cdot 3}{3 \cdot 2}$

Rewrite the expression.

$x = \frac{3}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{2}$

Decimal Form:

$x = 1.5$

Mixed Number Form:

$x = 1 \frac{1}{2}$

Solve for x |3x-4|=|3x-5|

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