Solve 2x + 3y - 4x - (y - x)/4 + (- x + y)/4 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$2x+3y-4x-\frac{y-x}{4}+\frac{-x+y}{4}$$

Evaluate

$3y-2x$

Short Solution Steps

Combine $2x$ and $-4x$ to get $-2x$.

$$-2x+3y-\frac{y-x}{4}+\frac{-x+y}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $-2x+3y$ times $\frac{4}{4}$.

$$\frac{4\left(-2x+3y\right)}{4}-\frac{y-x}{4}+\frac{-x+y}{4}$$

Since $\frac{4\left(-2x+3y\right)}{4}$ and $\frac{y-x}{4}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(-2x+3y\right)-\left(y-x\right)}{4}+\frac{-x+y}{4}$$

Do the multiplications in $4\left(-2x+3y\right)-\left(y-x\right)$.

$$\frac{-8x+12y-y+x}{4}+\frac{-x+y}{4}$$

Combine like terms in $-8x+12y-y+x$.

$$\frac{-7x+11y}{4}+\frac{-x+y}{4}$$

Since $\frac{-7x+11y}{4}$ and $\frac{-x+y}{4}$ have the same denominator, add them by adding their numerators.

$$\frac{-7x+11y-x+y}{4}$$

Combine like terms in $-7x+11y-x+y$.

$$\frac{-8x+12y}{4}$$

Divide each term of $-8x+12y$ by $4$ to get $-2x+3y$.

$$-2x+3y$$

Expand

$3y-2x$

Short Solution Steps

Combine $2x$ and $-4x$ to get $-2x$.

$$-2x+3y-\frac{y-x}{4}+\frac{-x+y}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $-2x+3y$ times $\frac{4}{4}$.

$$\frac{4\left(-2x+3y\right)}{4}-\frac{y-x}{4}+\frac{-x+y}{4}$$

Since $\frac{4\left(-2x+3y\right)}{4}$ and $\frac{y-x}{4}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(-2x+3y\right)-\left(y-x\right)}{4}+\frac{-x+y}{4}$$

Do the multiplications in $4\left(-2x+3y\right)-\left(y-x\right)$.

$$\frac{-8x+12y-y+x}{4}+\frac{-x+y}{4}$$

Combine like terms in $-8x+12y-y+x$.

$$\frac{-7x+11y}{4}+\frac{-x+y}{4}$$

Since $\frac{-7x+11y}{4}$ and $\frac{-x+y}{4}$ have the same denominator, add them by adding their numerators.

$$\frac{-7x+11y-x+y}{4}$$

Combine like terms in $-7x+11y-x+y$.

$$\frac{-8x+12y}{4}$$

Divide each term of $-8x+12y$ by $4$ to get $-2x+3y$.

$$-2x+3y$$