Solve 3/2(4x-3)=2(-4x-3)

$$\frac{ 3 }{ 2 } (4x-3)=2(-4x-3)$$

Solve for x

$$x=-\frac{3}{28}\approx -0.107142857$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{3}{2} by 4x-3.

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

Express \frac{3}{2}\times 4 as a single fraction.

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

Multiply 3 and 4 to get 12.

$$\frac{12}{2}x+\frac{3}{2}\left(-3\right)=2\left(-4x-3\right)$$

Divide 12 by 2 to get 6.

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

Express \frac{3}{2}\left(-3\right) as a single fraction.

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

Multiply 3 and -3 to get -9.

$$6x+\frac{-9}{2}=2\left(-4x-3\right)$$

Fraction \frac{-9}{2} can be rewritten as -\frac{9}{2} by extracting the negative sign.

$$6x-\frac{9}{2}=2\left(-4x-3\right)$$

Use the distributive property to multiply 2 by -4x-3.

$$6x-\frac{9}{2}=-8x-6$$

Add 8x to both sides.

$$6x-\frac{9}{2}+8x=-6$$

Combine 6x and 8x to get 14x.

$$14x-\frac{9}{2}=-6$$

Add \frac{9}{2} to both sides.

$$14x=-6+\frac{9}{2}$$

Convert -6 to fraction -\frac{12}{2}.

$$14x=-\frac{12}{2}+\frac{9}{2}$$

Since -\frac{12}{2} and \frac{9}{2} have the same denominator, add them by adding their numerators.

$$14x=\frac{-12+9}{2}$$

Add -12 and 9 to get -3.

$$14x=-\frac{3}{2}$$

Divide both sides by 14.

$$x=\frac{-\frac{3}{2}}{14}$$

Express \frac{-\frac{3}{2}}{14} as a single fraction.

$$x=\frac{-3}{2\times 14}$$

Multiply 2 and 14 to get 28.

$$x=\frac{-3}{28}$$

Fraction \frac{-3}{28} can be rewritten as -\frac{3}{28} by extracting the negative sign.

$$x=-\frac{3}{28}$$