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

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

Solve for x

$$x\geq 3$$

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.

$$5\left(7-x\right)-30\leq 2\left(3+4x\right)-40$$

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

$$35-5x-30\leq 2\left(3+4x\right)-40$$

Subtract 30 from 35 to get 5.

$$5-5x\leq 2\left(3+4x\right)-40$$

Use the distributive property to multiply 2 by 3+4x.

$$5-5x\leq 6+8x-40$$

Subtract 40 from 6 to get -34.

$$5-5x\leq -34+8x$$

Subtract 8x from both sides.

$$5-5x-8x\leq -34$$

Combine -5x and -8x to get -13x.

$$5-13x\leq -34$$

Subtract 5 from both sides.

$$-13x\leq -34-5$$

Subtract 5 from -34 to get -39.

$$-13x\leq -39$$

Divide both sides by -13. Since -13 is negative, the inequality direction is changed.

$$x\geq \frac{-39}{-13}$$

Divide -39 by -13 to get 3.

$$x\geq 3$$