Solve 5-2x/7leq3/2

$$\frac { 5 - 2 x } { 7 } \leq \frac { 3 } { 2 }$$

Solve for x

$$x\geq -\frac{11}{4}$$

Solution Steps

Multiply both sides by 7. Since 7 is positive, the inequality direction remains the same.

$$5-2x\leq \frac{3}{2}\times 7$$

Express \frac{3}{2}\times 7 as a single fraction.

$$5-2x\leq \frac{3\times 7}{2}$$

Multiply 3 and 7 to get 21.

$$5-2x\leq \frac{21}{2}$$

Subtract 5 from both sides.

$$-2x\leq \frac{21}{2}-5$$

Convert 5 to fraction \frac{10}{2}.

$$-2x\leq \frac{21}{2}-\frac{10}{2}$$

Since \frac{21}{2} and \frac{10}{2} have the same denominator, subtract them by subtracting their numerators.

$$-2x\leq \frac{21-10}{2}$$

Subtract 10 from 21 to get 11.

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

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

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

Express \frac{\frac{11}{2}}{-2} as a single fraction.

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

Multiply 2 and -2 to get -4.

$$x\geq \frac{11}{-4}$$

Fraction \frac{11}{-4} can be rewritten as -\frac{11}{4} by extracting the negative sign.

$$x\geq -\frac{11}{4}$$