Solve -5+x/3geq4x+1/8-31/2

$$- 5 + \frac { x } { 3 } \geq \frac { 4 x + 1 } { 8 } - 3 \frac { 1 } { 2 }$$

Solve for x

$$x\leq -\frac{39}{4}$$

Solution Steps

Multiply both sides of the equation by 24, the least common multiple of 3,8,2. Since 24 is positive, the inequality direction remains the same.

$$-120+8x\geq 3\left(4x+1\right)-12\left(3\times 2+1\right)$$

Use the distributive property to multiply 3 by 4x+1.

$$-120+8x\geq 12x+3-12\left(3\times 2+1\right)$$

Multiply 3 and 2 to get 6.

$$-120+8x\geq 12x+3-12\left(6+1\right)$$

Add 6 and 1 to get 7.

$$-120+8x\geq 12x+3-12\times 7$$

Multiply -12 and 7 to get -84.

$$-120+8x\geq 12x+3-84$$

Subtract 84 from 3 to get -81.

$$-120+8x\geq 12x-81$$

Subtract 12x from both sides.

$$-120+8x-12x\geq -81$$

Combine 8x and -12x to get -4x.

$$-120-4x\geq -81$$

Add 120 to both sides.

$$-4x\geq -81+120$$

Add -81 and 120 to get 39.

$$-4x\geq 39$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x\leq -\frac{39}{4}$$