Solve (2x + 4)/3 - (3x - 42)/4 = (4x - 24)/5 - (5x - 40)/6 | 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

$$\frac{2x+4}{3}-\frac{3x-42}{4}=\frac{4x-24}{5}-\frac{5x-40}{6}$$

Solve for x

$x = \frac{598}{3} = 199\frac{1}{3} \approx 199.333333333$

Steps for Solving Linear Equation

Multiply both sides of the equation by $60$, the least common multiple of $3,4,5,6$.

$$20\left(2x+4\right)-15\left(3x-42\right)=12\left(4x-24\right)-10\left(5x-40\right)$$

Use the distributive property to multiply $20$ by $2x+4$.

$$40x+80-15\left(3x-42\right)=12\left(4x-24\right)-10\left(5x-40\right)$$

Use the distributive property to multiply $-15$ by $3x-42$.

$$40x+80-45x+630=12\left(4x-24\right)-10\left(5x-40\right)$$

Combine $40x$ and $-45x$ to get $-5x$.

$$-5x+80+630=12\left(4x-24\right)-10\left(5x-40\right)$$

Add $80$ and $630$ to get $710$.

$$-5x+710=12\left(4x-24\right)-10\left(5x-40\right)$$

Use the distributive property to multiply $12$ by $4x-24$.

$$-5x+710=48x-288-10\left(5x-40\right)$$

Use the distributive property to multiply $-10$ by $5x-40$.

$$-5x+710=48x-288-50x+400$$

Combine $48x$ and $-50x$ to get $-2x$.

$$-5x+710=-2x-288+400$$

Add $-288$ and $400$ to get $112$.

$$-5x+710=-2x+112$$

Add $2x$ to both sides.

$$-5x+710+2x=112$$

Combine $-5x$ and $2x$ to get $-3x$.

$$-3x+710=112$$

Subtract $710$ from both sides.

$$-3x=112-710$$

Subtract $710$ from $112$ to get $-598$.

$$-3x=-598$$

Divide both sides by $-3$.

$$x=\frac{-598}{-3}$$

Fraction $\frac{-598}{-3}$ can be simplified to $\frac{598}{3}$ by removing the negative sign from both the numerator and the denominator.

$$x=\frac{598}{3}$$