Solve 1/2left(x+5right)+3left(1-2xright)<1

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

Solve for x

$$x>\frac{9}{11}$$

Solution Steps

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

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

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

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

Use the distributive property to multiply 3 by 1-2x.

$$\frac{1}{2}x+\frac{5}{2}+3-6x<1$$

Convert 3 to fraction \frac{6}{2}.

$$\frac{1}{2}x+\frac{5}{2}+\frac{6}{2}-6x<1$$

Since \frac{5}{2} and \frac{6}{2} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}x+\frac{5+6}{2}-6x<1$$

Add 5 and 6 to get 11.

$$\frac{1}{2}x+\frac{11}{2}-6x<1$$

Combine \frac{1}{2}x and -6x to get -\frac{11}{2}x.

$$-\frac{11}{2}x+\frac{11}{2}<1$$

Subtract \frac{11}{2} from both sides.

$$-\frac{11}{2}x<1-\frac{11}{2}$$

Convert 1 to fraction \frac{2}{2}.

$$-\frac{11}{2}x<\frac{2}{2}-\frac{11}{2}$$

Since \frac{2}{2} and \frac{11}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{11}{2}x<\frac{2-11}{2}$$

Subtract 11 from 2 to get -9.

$$-\frac{11}{2}x<-\frac{9}{2}$$

Multiply both sides by -\frac{2}{11}, the reciprocal of -\frac{11}{2}. Since -\frac{11}{2} is negative, the inequality direction is changed.

$$x>-\frac{9}{2}\left(-\frac{2}{11}\right)$$

Multiply -\frac{9}{2} times -\frac{2}{11} by multiplying numerator times numerator and denominator times denominator.

$$x>\frac{-9\left(-2\right)}{2\times 11}$$

Do the multiplications in the fraction \frac{-9\left(-2\right)}{2\times 11}.

$$x>\frac{18}{22}$$

Reduce the fraction \frac{18}{22} to lowest terms by extracting and canceling out 2.

$$x>\frac{9}{11}$$