Solve (x-5)(4-x)+(2-(x)/(2))(x+3)== | 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

$$(x-5)(4-x)+(2- \frac{ x }{ 2 } )(x+3)==$$

Evaluate

$-\frac{3x^{2}}{2}+\frac{19x}{2}-14$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply $2$ times $\frac{2}{2}$.

$$\left(x-5\right)\left(4-x\right)+\left(\frac{2\times 2}{2}-\frac{x}{2}\right)\left(x+3\right)$$

Since $\frac{2\times 2}{2}$ and $\frac{x}{2}$ have the same denominator, subtract them by subtracting their numerators.

$$\left(x-5\right)\left(4-x\right)+\frac{2\times 2-x}{2}\left(x+3\right)$$

Do the multiplications in $2\times 2-x$.

$$\left(x-5\right)\left(4-x\right)+\frac{4-x}{2}\left(x+3\right)$$

Express $\frac{4-x}{2}\left(x+3\right)$ as a single fraction.

$$\left(x-5\right)\left(4-x\right)+\frac{\left(4-x\right)\left(x+3\right)}{2}$$

Apply the distributive property by multiplying each term of $x-5$ by each term of $4-x$.

$$4x-x^{2}-20+5x+\frac{\left(4-x\right)\left(x+3\right)}{2}$$

Combine $4x$ and $5x$ to get $9x$.

$$9x-x^{2}-20+\frac{\left(4-x\right)\left(x+3\right)}{2}$$

Apply the distributive property by multiplying each term of $4-x$ by each term of $x+3$.

$$9x-x^{2}-20+\frac{4x+12-x^{2}-3x}{2}$$

Combine $4x$ and $-3x$ to get $x$.

$$9x-x^{2}-20+\frac{x+12-x^{2}}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $9x-x^{2}-20$ times $\frac{2}{2}$.

$$\frac{2\left(9x-x^{2}-20\right)}{2}+\frac{x+12-x^{2}}{2}$$

Since $\frac{2\left(9x-x^{2}-20\right)}{2}$ and $\frac{x+12-x^{2}}{2}$ have the same denominator, add them by adding their numerators.

$$\frac{2\left(9x-x^{2}-20\right)+x+12-x^{2}}{2}$$

Do the multiplications in $2\left(9x-x^{2}-20\right)+x+12-x^{2}$.

$$\frac{18x-2x^{2}-40+x+12-x^{2}}{2}$$

Combine like terms in $18x-2x^{2}-40+x+12-x^{2}$.

$$\frac{19x-3x^{2}-28}{2}$$

Expand

$-\frac{3x^{2}}{2}+\frac{19x}{2}-14$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply $2$ times $\frac{2}{2}$.

$$\left(x-5\right)\left(4-x\right)+\left(\frac{2\times 2}{2}-\frac{x}{2}\right)\left(x+3\right)$$

Since $\frac{2\times 2}{2}$ and $\frac{x}{2}$ have the same denominator, subtract them by subtracting their numerators.

$$\left(x-5\right)\left(4-x\right)+\frac{2\times 2-x}{2}\left(x+3\right)$$

Do the multiplications in $2\times 2-x$.

$$\left(x-5\right)\left(4-x\right)+\frac{4-x}{2}\left(x+3\right)$$

Express $\frac{4-x}{2}\left(x+3\right)$ as a single fraction.

$$\left(x-5\right)\left(4-x\right)+\frac{\left(4-x\right)\left(x+3\right)}{2}$$

Apply the distributive property by multiplying each term of $x-5$ by each term of $4-x$.

$$4x-x^{2}-20+5x+\frac{\left(4-x\right)\left(x+3\right)}{2}$$

Combine $4x$ and $5x$ to get $9x$.

$$9x-x^{2}-20+\frac{\left(4-x\right)\left(x+3\right)}{2}$$

Apply the distributive property by multiplying each term of $4-x$ by each term of $x+3$.

$$9x-x^{2}-20+\frac{4x+12-x^{2}-3x}{2}$$

Combine $4x$ and $-3x$ to get $x$.

$$9x-x^{2}-20+\frac{x+12-x^{2}}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $9x-x^{2}-20$ times $\frac{2}{2}$.

$$\frac{2\left(9x-x^{2}-20\right)}{2}+\frac{x+12-x^{2}}{2}$$

Since $\frac{2\left(9x-x^{2}-20\right)}{2}$ and $\frac{x+12-x^{2}}{2}$ have the same denominator, add them by adding their numerators.

$$\frac{2\left(9x-x^{2}-20\right)+x+12-x^{2}}{2}$$

Do the multiplications in $2\left(9x-x^{2}-20\right)+x+12-x^{2}$.

$$\frac{18x-2x^{2}-40+x+12-x^{2}}{2}$$

Combine like terms in $18x-2x^{2}-40+x+12-x^{2}$.

$$\frac{19x-3x^{2}-28}{2}$$