Solve (-3/2)^-2=2*(-3+2x)

$$( - \frac { 3 } { 2 } ) ^ { - 2 } = 2 \cdot ( - 3 + 2 x )$$

Solve for x

$$x = \frac{29}{18} = 1\frac{11}{18} \approx 1.611111111$$

Steps for Solving Linear Equation

Calculate -\frac{3}{2} to the power of -2 and get \frac{4}{9}.

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

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

$$\frac{4}{9}=-6+4x$$

Swap sides so that all variable terms are on the left hand side.

$$-6+4x=\frac{4}{9}$$

Add 6 to both sides.

$$4x=\frac{4}{9}+6$$

Add \frac{4}{9} and 6 to get \frac{58}{9}.

$$4x=\frac{58}{9}$$

Divide both sides by 4.

$$x=\frac{\frac{58}{9}}{4}$$

Express \frac{\frac{58}{9}}{4} as a single fraction.

$$x=\frac{58}{9\times 4}$$

Multiply 9 and 4 to get 36.

$$x=\frac{58}{36}$$

Reduce the fraction \frac{58}{36} to lowest terms by extracting and canceling out 2.

$$x=\frac{29}{18}$$