Solve 5(3x+1/2)=-10(1-3x)

$$5 ( 3 x + \frac { 1 } { 2 } ) = - 10 ( 1 - 3 x )$$

Solve for x

$$x=\frac{5}{6}\approx 0.833333333$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by 3x+\frac{1}{2}.

$$15x+5\times \frac{1}{2}=-10\left(1-3x\right)$$

Multiply 5 and \frac{1}{2} to get \frac{5}{2}.

$$15x+\frac{5}{2}=-10\left(1-3x\right)$$

Use the distributive property to multiply -10 by 1-3x.

$$15x+\frac{5}{2}=-10+30x$$

Subtract 30x from both sides.

$$15x+\frac{5}{2}-30x=-10$$

Combine 15x and -30x to get -15x.

$$-15x+\frac{5}{2}=-10$$

Subtract \frac{5}{2} from both sides.

$$-15x=-10-\frac{5}{2}$$

Convert -10 to fraction -\frac{20}{2}.

$$-15x=-\frac{20}{2}-\frac{5}{2}$$

Since -\frac{20}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

$$-15x=\frac{-20-5}{2}$$

Subtract 5 from -20 to get -25.

$$-15x=-\frac{25}{2}$$

Divide both sides by -15.

$$x=\frac{-\frac{25}{2}}{-15}$$

Express \frac{-\frac{25}{2}}{-15} as a single fraction.

$$x=\frac{-25}{2\left(-15\right)}$$

Multiply 2 and -15 to get -30.

$$x=\frac{-25}{-30}$$

Reduce the fraction \frac{-25}{-30} to lowest terms by extracting and canceling out -5.

$$x=\frac{5}{6}$$