Solve 1/2x-1<5-x

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

Solve for x

$$x<4$$

Solution Steps

Add x to both sides.

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

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

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

Add 1 to both sides.

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

Add 5 and 1 to get 6.

$$\frac{3}{2}x<6$$

Multiply both sides by \frac{2}{3}, the reciprocal of \frac{3}{2}. Since \frac{3}{2} is positive, the inequality direction remains the same.

$$x<6\times \frac{2}{3}$$

Express 6\times \frac{2}{3} as a single fraction.

$$x<\frac{6\times 2}{3}$$

Multiply 6 and 2 to get 12.

$$x<\frac{12}{3}$$

Divide 12 by 3 to get 4.

$$x<4$$