Solve 4x+7geq7x+1/2

$$4 x + 7 \geq 7 x + \frac { 1 } { 2 }$$

Solve for x

$$x\leq \frac{13}{6}$$

Solution Steps

Subtract 7x from both sides.

$$4x+7-7x\geq \frac{1}{2}$$

Combine 4x and -7x to get -3x.

$$-3x+7\geq \frac{1}{2}$$

Subtract 7 from both sides.

$$-3x\geq \frac{1}{2}-7$$

Convert 7 to fraction \frac{14}{2}.

$$-3x\geq \frac{1}{2}-\frac{14}{2}$$

Since \frac{1}{2} and \frac{14}{2} have the same denominator, subtract them by subtracting their numerators.

$$-3x\geq \frac{1-14}{2}$$

Subtract 14 from 1 to get -13.

$$-3x\geq -\frac{13}{2}$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$x\leq \frac{-\frac{13}{2}}{-3}$$

Express \frac{-\frac{13}{2}}{-3} as a single fraction.

$$x\leq \frac{-13}{2\left(-3\right)}$$

Multiply 2 and -3 to get -6.

$$x\leq \frac{-13}{-6}$$

Fraction \frac{-13}{-6} can be simplified to \frac{13}{6} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{13}{6}$$