Solve 3(4x-1)-7(2x+4)=x-0.5

$$3(4x-1)-7(2x+4)=x-0.5$$

Solve for x

$$x = -\frac{61}{6} = -10\frac{1}{6} \approx -10.166666667$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by 4x-1.

$$12x-3-7\left(2x+4\right)=x-0.5$$

Use the distributive property to multiply -7 by 2x+4.

$$12x-3-14x-28=x-0.5$$

Combine 12x and -14x to get -2x.

$$-2x-3-28=x-0.5$$

Subtract 28 from -3 to get -31.

$$-2x-31=x-0.5$$

Subtract x from both sides.

$$-2x-31-x=-0.5$$

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

$$-3x-31=-0.5$$

Add 31 to both sides.

$$-3x=-0.5+31$$

Add -0.5 and 31 to get 30.5.

$$-3x=30.5$$

Divide both sides by -3.

$$x=\frac{30.5}{-3}$$

Expand \frac{30.5}{-3} by multiplying both numerator and the denominator by 10.

$$x=\frac{305}{-30}$$

Reduce the fraction \frac{305}{-30} to lowest terms by extracting and canceling out 5.

$$x=-\frac{61}{6}$$