Solve for x |3(x-4)+7|=|3x-5|

$| 3 (x - 4) + 7 | = | 3 x - 5 |$

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

$3 (x - 4) + 7 = 3 x - 5$

$3 (x - 4) + 7 = - (3 x - 5)$

$- (3 (x - 4) + 7) = 3 x - 5$

$- (3 (x - 4) + 7) = - (3 x - 5)$

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

$3 (x - 4) + 7 = 3 x - 5$

$3 (x - 4) + 7 = - (3 x - 5)$

Solve $3 (x - 4) + 7 = 3 x - 5$ for $x$ .

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Simplify $3 (x - 4) + 7$ .

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Simplify each term.

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Apply the distributive property.

$3 x + 3 \cdot - 4 + 7 = 3 x - 5$

Multiply $3$ by $- 4$ .

$3 x - 12 + 7 = 3 x - 5$

Add $- 12$ and $7$ .

$3 x - 5 = 3 x - 5$

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

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

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

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

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Subtract $3 x$ from $3 x$ .

$0 - 5 = - 5$

Subtract $5$ from $0$ .

$- 5 = - 5$

Since $- 5 = - 5$ , the equation will always be true.

All real numbers

Solve $3 (x - 4) + 7 = - (3 x - 5)$ for $x$ .

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Simplify $3 (x - 4) + 7$ .

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Simplify each term.

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Apply the distributive property.

$3 x + 3 \cdot - 4 + 7 = - (3 x - 5)$

Multiply $3$ by $- 4$ .

$3 x - 12 + 7 = - (3 x - 5)$

Add $- 12$ and $7$ .

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

Simplify $- (3 x - 5)$ .

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Apply the distributive property.

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

Multiply.

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Multiply $3$ by $- 1$ .

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

Multiply $- 1$ by $- 5$ .

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

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

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

$3 x - 5 + 3 x = 5$

Add $3 x$ and $3 x$ .

$6 x - 5 = 5$

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

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Add $5$ to both sides of the equation.

$6 x = 5 + 5$

Add $5$ and $5$ .

$6 x = 10$

Divide each term by $6$ and simplify.

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Divide each term in $6 x = 10$ by $6$ .

$\frac{6 x}{6} = \frac{10}{6}$

Cancel the common factor of $6$ .

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Cancel the common factor.

$\frac{6 x}{6} = \frac{10}{6}$

Divide $x$ by $1$ .

$x = \frac{10}{6}$

Cancel the common factor of $10$ and $6$ .

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Factor $2$ out of $10$ .

$x = \frac{2 (5)}{6}$

Cancel the common factors.

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Factor $2$ out of $6$ .

$x = \frac{2 \cdot 5}{2 \cdot 3}$

Cancel the common factor.

$x = \frac{2 \cdot 5}{2 \cdot 3}$

Rewrite the expression.

$x = \frac{5}{3}$

List all of the solutions.

$x =, \frac{5}{3}$

Verify each of the solutions by substituting them into $| 3 (x - 4) + 7 | = | 3 x - 5 |$ and solving.

$x = \frac{5}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{3}$

Decimal Form:

$x = 1.\overline{6}$

Mixed Number Form:

$x = 1 \frac{2}{3}$

Solve for x |3(x-4)+7|=|3x-5|

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