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

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

Solve for x

$x = \frac{12}{5} = 2\frac{2}{5} = 2.4$

Steps for Solving Linear Equation

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

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

Multiply $2$ and $2$ to get $4$.

$$4x+6=3\times 3x-6$$

Multiply $3$ and $3$ to get $9$.

$$4x+6=9x-6$$

Subtract $9x$ from both sides.

$$4x+6-9x=-6$$

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

$$-5x+6=-6$$

Subtract $6$ from both sides.

$$-5x=-6-6$$

Subtract $6$ from $-6$ to get $-12$.

$$-5x=-12$$

Divide both sides by $-5$.

$$x=\frac{-12}{-5}$$

Fraction $\frac{-12}{-5}$ can be simplified to $\frac{12}{5}$ by removing the negative sign from both the numerator and the denominator.

$$x=\frac{12}{5}$$