Solve 10x+3leq5x-1/2

$$10x+3 \leq 5x- \frac{ 1 }{ 2 }$$

Solve for x

$$x\leq -\frac{7}{10}$$

Solution Steps

Subtract 5x from both sides.

$$10x+3-5x\leq -\frac{1}{2}$$

Combine 10x and -5x to get 5x.

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

Subtract 3 from both sides.

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

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

$$5x\leq -\frac{1}{2}-\frac{6}{2}$$

Since -\frac{1}{2} and \frac{6}{2} have the same denominator, subtract them by subtracting their numerators.

$$5x\leq \frac{-1-6}{2}$$

Subtract 6 from -1 to get -7.

$$5x\leq -\frac{7}{2}$$

Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.

$$x\leq \frac{-\frac{7}{2}}{5}$$

Express \frac{-\frac{7}{2}}{5} as a single fraction.

$$x\leq \frac{-7}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$x\leq \frac{-7}{10}$$

Fraction \frac{-7}{10} can be rewritten as -\frac{7}{10} by extracting the negative sign.

$$x\leq -\frac{7}{10}$$