Solve pape Date : 3(2 - x) - 4 <= 2(x - 3) + 5x | 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

$$3 ( 2 - x ) - 4 : ( 2 ( x - 3 ) + 5 x$$

Evaluate

$\frac{-21x^{2}+60x-40}{7x-6}$

Short Solution Steps

Use the distributive property to multiply $3$ by $2-x$.

$$6-3x-\frac{4}{2\left(x-3\right)+5x}$$

Use the distributive property to multiply $2$ by $x-3$.

$$6-3x-\frac{4}{2x-6+5x}$$

Combine $2x$ and $5x$ to get $7x$.

$$6-3x-\frac{4}{7x-6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $6-3x$ times $\frac{7x-6}{7x-6}$.

$$\frac{\left(6-3x\right)\left(7x-6\right)}{7x-6}-\frac{4}{7x-6}$$

Since $\frac{\left(6-3x\right)\left(7x-6\right)}{7x-6}$ and $\frac{4}{7x-6}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(6-3x\right)\left(7x-6\right)-4}{7x-6}$$

Do the multiplications in $\left(6-3x\right)\left(7x-6\right)-4$.

$$\frac{42x-36-21x^{2}+18x-4}{7x-6}$$

Combine like terms in $42x-36-21x^{2}+18x-4$.

$$\frac{60x-40-21x^{2}}{7x-6}$$

Expand

$\frac{-21x^{2}+60x-40}{7x-6}$

Short Solution Steps

Use the distributive property to multiply $3$ by $2-x$.

$$6-3x-\frac{4}{2\left(x-3\right)+5x}$$

Use the distributive property to multiply $2$ by $x-3$.

$$6-3x-\frac{4}{2x-6+5x}$$

Combine $2x$ and $5x$ to get $7x$.

$$6-3x-\frac{4}{7x-6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $6-3x$ times $\frac{7x-6}{7x-6}$.

$$\frac{\left(6-3x\right)\left(7x-6\right)}{7x-6}-\frac{4}{7x-6}$$

Since $\frac{\left(6-3x\right)\left(7x-6\right)}{7x-6}$ and $\frac{4}{7x-6}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(6-3x\right)\left(7x-6\right)-4}{7x-6}$$

Do the multiplications in $\left(6-3x\right)\left(7x-6\right)-4$.

$$\frac{42x-36-21x^{2}+18x-4}{7x-6}$$

Combine like terms in $42x-36-21x^{2}+18x-4$.

$$\frac{60x-40-21x^{2}}{7x-6}$$