Solve 5-4x/4+9x-21/2geq2+10x-37/4

$$\frac{ 5-4x }{ 4 } + \frac{ 9x-21 }{ 2 } \geq 2+ \frac{ 10x-37 }{ 4 }$$

Solve for x

$$x\geq 2$$

Solution Steps

Multiply both sides of the equation by 4, the least common multiple of 4,2. Since 4 is positive, the inequality direction remains the same.

$$5-4x+2\left(9x-21\right)\geq 8+10x-37$$

Use the distributive property to multiply 2 by 9x-21.

$$5-4x+18x-42\geq 8+10x-37$$

Combine -4x and 18x to get 14x.

$$5+14x-42\geq 8+10x-37$$

Subtract 42 from 5 to get -37.

$$-37+14x\geq 8+10x-37$$

Subtract 37 from 8 to get -29.

$$-37+14x\geq -29+10x$$

Subtract 10x from both sides.

$$-37+14x-10x\geq -29$$

Combine 14x and -10x to get 4x.

$$-37+4x\geq -29$$

Add 37 to both sides.

$$4x\geq -29+37$$

Add -29 and 37 to get 8.

$$4x\geq 8$$

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

$$x\geq \frac{8}{4}$$

Divide 8 by 4 to get 2.

$$x\geq 2$$