Solve 1/2x-1<0.1x+1/2=

$$\frac{ 1 }{ 2 } x-1 < 0.1x+ \frac{ 1 }{ 2 } =$$

Solve for x

$$x<\frac{15}{4}$$

Solution Steps

Subtract 0.1x from both sides.

$$\frac{1}{2}x-1-0.1x<\frac{1}{2}$$

Combine \frac{1}{2}x and -0.1x to get \frac{2}{5}x.

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

Add 1 to both sides.

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

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

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

Since \frac{1}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

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

Add 1 and 2 to get 3.

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

Multiply both sides by \frac{5}{2}, the reciprocal of \frac{2}{5}. Since \frac{2}{5} is positive, the inequality direction remains the same.

$$x<\frac{3}{2}\times \frac{5}{2}$$

Multiply \frac{3}{2} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$x<\frac{3\times 5}{2\times 2}$$

Do the multiplications in the fraction \frac{3\times 5}{2\times 2}.

$$x<\frac{15}{4}$$