Solve (6x+1)/(3)=(5x-2)/(2) | 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

$$\frac{ 6x+1 }{ 3 } = \frac{ 5x-2 }{ 2 }$$

Solve for x

$x = \frac{8}{3} = 2\frac{2}{3} \approx 2.666666667$

Steps for Solving Linear Equation

Multiply both sides of the equation by $6$, the least common multiple of $3,2$.

$$2\left(6x+1\right)=3\left(5x-2\right)$$

Use the distributive property to multiply $2$ by $6x+1$.

$$12x+2=3\left(5x-2\right)$$

Use the distributive property to multiply $3$ by $5x-2$.

$$12x+2=15x-6$$

Subtract $15x$ from both sides.

$$12x+2-15x=-6$$

Combine $12x$ and $-15x$ to get $-3x$.

$$-3x+2=-6$$

Subtract $2$ from both sides.

$$-3x=-6-2$$

Subtract $2$ from $-6$ to get $-8$.

$$-3x=-8$$

Divide both sides by $-3$.

$$x=\frac{-8}{-3}$$

Fraction $\frac{-8}{-3}$ can be simplified to $\frac{8}{3}$ by removing the negative sign from both the numerator and the denominator.

$$x=\frac{8}{3}$$