Solve -5x+2(11/3-4/3x)=-31

$$-5x+2( \frac{ 11 }{ 3 } - \frac{ 4 }{ 3 } x)=-31$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by \frac{11}{3}-\frac{4}{3}x.

$$-5x+2\times \frac{11}{3}+2\left(-\frac{4}{3}\right)x=-31$$

Express 2\times \frac{11}{3} as a single fraction.

$$-5x+\frac{2\times 11}{3}+2\left(-\frac{4}{3}\right)x=-31$$

Multiply 2 and 11 to get 22.

$$-5x+\frac{22}{3}+2\left(-\frac{4}{3}\right)x=-31$$

Express 2\left(-\frac{4}{3}\right) as a single fraction.

$$-5x+\frac{22}{3}+\frac{2\left(-4\right)}{3}x=-31$$

Multiply 2 and -4 to get -8.

$$-5x+\frac{22}{3}+\frac{-8}{3}x=-31$$

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$-5x+\frac{22}{3}-\frac{8}{3}x=-31$$

Combine -5x and -\frac{8}{3}x to get -\frac{23}{3}x.

$$-\frac{23}{3}x+\frac{22}{3}=-31$$

Subtract \frac{22}{3} from both sides.

$$-\frac{23}{3}x=-31-\frac{22}{3}$$

Convert -31 to fraction -\frac{93}{3}.

$$-\frac{23}{3}x=-\frac{93}{3}-\frac{22}{3}$$

Since -\frac{93}{3} and \frac{22}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{23}{3}x=\frac{-93-22}{3}$$

Subtract 22 from -93 to get -115.

$$-\frac{23}{3}x=-\frac{115}{3}$$

Multiply both sides by -\frac{3}{23}, the reciprocal of -\frac{23}{3}.

$$x=-\frac{115}{3}\left(-\frac{3}{23}\right)$$

Multiply -\frac{115}{3} times -\frac{3}{23} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-115\left(-3\right)}{3\times 23}$$

Do the multiplications in the fraction \frac{-115\left(-3\right)}{3\times 23}.

$$x=\frac{345}{69}$$

Divide 345 by 69 to get 5.

$$x=5$$