Solve 7-x/2-3leq3+5x/5-4

$$\frac { 7 - x } { 2 } - 3 \leq \frac { 3 + 5 x } { 5 } - 4$$

Solve for x

$$x\geq \frac{13}{5}$$

Solution Steps

Multiply both sides of the equation by 10, the least common multiple of 2,5. Since 10 is positive, the inequality direction remains the same.

$$5\left(7-x\right)-30\leq 2\left(3+5x\right)-40$$

Use the distributive property to multiply 5 by 7-x.

$$35-5x-30\leq 2\left(3+5x\right)-40$$

Subtract 30 from 35 to get 5.

$$5-5x\leq 2\left(3+5x\right)-40$$

Use the distributive property to multiply 2 by 3+5x.

$$5-5x\leq 6+10x-40$$

Subtract 40 from 6 to get -34.

$$5-5x\leq -34+10x$$

Subtract 10x from both sides.

$$5-5x-10x\leq -34$$

Combine -5x and -10x to get -15x.

$$5-15x\leq -34$$

Subtract 5 from both sides.

$$-15x\leq -34-5$$

Subtract 5 from -34 to get -39.

$$-15x\leq -39$$

Divide both sides by -15. Since -15 is negative, the inequality direction is changed.

$$x\geq \frac{-39}{-15}$$

Reduce the fraction \frac{-39}{-15} to lowest terms by extracting and canceling out -3.

$$x\geq \frac{13}{5}$$