Basic Math Examples

$| 5 y - 2 | = | 53 - 6 y |$

Step 1

Rewrite the equation as $| 53 - 6 y | = | 5 y - 2 |$ .

$| 53 - 6 y | = | 5 y - 2 |$

Step 2

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

$53 - 6 y = 5 y - 2$

$53 - 6 y = - (5 y - 2)$

$- (53 - 6 y) = 5 y - 2$

$- (53 - 6 y) = - (5 y - 2)$

Step 3

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

$53 - 6 y = 5 y - 2$

$53 - 6 y = - (5 y - 2)$

Step 4

Solve $53 - 6 y = 5 y - 2$ for $y$ .

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Step 4.1

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

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Step 4.1.1

Subtract $5 y$ from both sides of the equation.

$53 - 6 y - 5 y = - 2$

Step 4.1.2

Subtract $5 y$ from $- 6 y$ .

$53 - 11 y = - 2$

Step 4.2

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

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Step 4.2.1

Subtract $53$ from both sides of the equation.

$- 11 y = - 2 - 53$

Step 4.2.2

Subtract $53$ from $- 2$ .

$- 11 y = - 55$

Step 4.3

Divide each term in $- 11 y = - 55$ by $- 11$ and simplify.

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Step 4.3.1

Divide each term in $- 11 y = - 55$ by $- 11$ .

$\frac{- 11 y}{- 11} = \frac{- 55}{- 11}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $- 11$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 11 y}{- 11} = \frac{- 55}{- 11}$

Step 4.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 55}{- 11}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $- 55$ by $- 11$ .

$y = 5$

Step 5

Solve $53 - 6 y = - (5 y - 2)$ for $y$ .

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Step 5.1

Simplify $- (5 y - 2)$ .

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Step 5.1.1

Rewrite.

$53 - 6 y = 0 + 0 - (5 y - 2)$

Step 5.1.2

Simplify by adding zeros.

$53 - 6 y = - (5 y - 2)$

Step 5.1.3

Apply the distributive property.

$53 - 6 y = - (5 y) - - 2$

Step 5.1.4

Multiply.

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Step 5.1.4.1

Multiply $5$ by $- 1$ .

$53 - 6 y = - 5 y - - 2$

Step 5.1.4.2

Multiply $- 1$ by $- 2$ .

$53 - 6 y = - 5 y + 2$

Step 5.2

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

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Step 5.2.1

Add $5 y$ to both sides of the equation.

$53 - 6 y + 5 y = 2$

Step 5.2.2

Add $- 6 y$ and $5 y$ .

$53 - y = 2$

Step 5.3

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

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Step 5.3.1

Subtract $53$ from both sides of the equation.

$- y = 2 - 53$

Step 5.3.2

Subtract $53$ from $2$ .

$- y = - 51$

Step 5.4

Divide each term in $- y = - 51$ by $- 1$ and simplify.

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Step 5.4.1

Divide each term in $- y = - 51$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 51}{- 1}$

Step 5.4.2

Simplify the left side.

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Step 5.4.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 51}{- 1}$

Step 5.4.2.2

Divide $y$ by $1$ .

$y = \frac{- 51}{- 1}$

Step 5.4.3

Simplify the right side.

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Step 5.4.3.1

Divide $- 51$ by $- 1$ .

$y = 51$

Step 6

List all of the solutions.

$y = 5, 51$