Solve -3x-(1/2x+1/3)=4x+10

$$- 3 x - ( 1 / 2 x + 1 / 3 ) = 4 x + 10$$

Solve for x

$$x = -\frac{62}{45} = -1\frac{17}{45} \approx -1.377777778$$

Steps for Solving Linear Equation

To find the opposite of \frac{1}{2}x+\frac{1}{3}, find the opposite of each term.

$$-3x-\frac{1}{2}x-\frac{1}{3}=4x+10$$

Combine -3x and -\frac{1}{2}x to get -\frac{7}{2}x.

$$-\frac{7}{2}x-\frac{1}{3}=4x+10$$

Subtract 4x from both sides.

$$-\frac{7}{2}x-\frac{1}{3}-4x=10$$

Combine -\frac{7}{2}x and -4x to get -\frac{15}{2}x.

$$-\frac{15}{2}x-\frac{1}{3}=10$$

Add \frac{1}{3} to both sides.

$$-\frac{15}{2}x=10+\frac{1}{3}$$

Convert 10 to fraction \frac{30}{3}.

$$-\frac{15}{2}x=\frac{30}{3}+\frac{1}{3}$$

Since \frac{30}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$-\frac{15}{2}x=\frac{30+1}{3}$$

Add 30 and 1 to get 31.

$$-\frac{15}{2}x=\frac{31}{3}$$

Multiply both sides by -\frac{2}{15}, the reciprocal of -\frac{15}{2}.

$$x=\frac{31}{3}\left(-\frac{2}{15}\right)$$

Multiply \frac{31}{3} times -\frac{2}{15} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{31\left(-2\right)}{3\times 15}$$

Do the multiplications in the fraction \frac{31\left(-2\right)}{3\times 15}.

$$x=\frac{-62}{45}$$

Fraction \frac{-62}{45} can be rewritten as -\frac{62}{45} by extracting the negative sign.

$$x=-\frac{62}{45}$$