Solve 3x - 5y - 2[5x - \{2x - 3(x - 3y) - 5x + y\}]

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Question

$$3x-5y-2[5x-\{2x-3(x-3y)-5x+y\}]$$

Evaluate

$15y-19x$

Solution Steps

Use the distributive property to multiply $-3$ by $x-3y$.

$$3x-5y-2\left(5x-\left(2x-3x+9y-5x+y\right)\right)$$

Combine $2x$ and $-3x$ to get $-x$.

$$3x-5y-2\left(5x-\left(-x+9y-5x+y\right)\right)$$

Combine $-x$ and $-5x$ to get $-6x$.

$$3x-5y-2\left(5x-\left(-6x+9y+y\right)\right)$$

Combine $9y$ and $y$ to get $10y$.

$$3x-5y-2\left(5x-\left(-6x+10y\right)\right)$$

To find the opposite of $-6x+10y$, find the opposite of each term.

$$3x-5y-2\left(5x-\left(-6x\right)-10y\right)$$

The opposite of $-6x$ is $6x$.

$$3x-5y-2\left(5x+6x-10y\right)$$

Combine $5x$ and $6x$ to get $11x$.

$$3x-5y-2\left(11x-10y\right)$$

Use the distributive property to multiply $-2$ by $11x-10y$.

$$3x-5y-22x+20y$$

Combine $3x$ and $-22x$ to get $-19x$.

$$-19x-5y+20y$$

Combine $-5y$ and $20y$ to get $15y$.

$$-19x+15y$$

Show Solution

Expand

$15y-19x$

Solution Steps

Use the distributive property to multiply $-3$ by $x-3y$.

$$3x-5y-2\left(5x-\left(2x-3x+9y-5x+y\right)\right)$$

Combine $2x$ and $-3x$ to get $-x$.

$$3x-5y-2\left(5x-\left(-x+9y-5x+y\right)\right)$$

Combine $-x$ and $-5x$ to get $-6x$.

$$3x-5y-2\left(5x-\left(-6x+9y+y\right)\right)$$

Combine $9y$ and $y$ to get $10y$.

$$3x-5y-2\left(5x-\left(-6x+10y\right)\right)$$

To find the opposite of $-6x+10y$, find the opposite of each term.

$$3x-5y-2\left(5x-\left(-6x\right)-10y\right)$$

The opposite of $-6x$ is $6x$.

$$3x-5y-2\left(5x+6x-10y\right)$$

Combine $5x$ and $6x$ to get $11x$.

$$3x-5y-2\left(11x-10y\right)$$

Use the distributive property to multiply $-2$ by $11x-10y$.

$$3x-5y-22x+20y$$

Combine $3x$ and $-22x$ to get $-19x$.

$$-19x-5y+20y$$

Combine $-5y$ and $20y$ to get $15y$.

$$-19x+15y$$

Show Solution

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Example

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Solution Steps