Solve 292x-(x+2)/33geqx+1/4

$$\frac { 292 x - ( x + 2 ) } { 33 } \geq \frac { x + 1 } { 4 }$$

Solve for x

$$x\geq \frac{41}{1131}$$

Solution Steps

Multiply both sides of the equation by 132, the least common multiple of 33,4. Since 132 is positive, the inequality direction remains the same.

$$4\left(292x-\left(x+2\right)\right)\geq 33\left(x+1\right)$$

To find the opposite of x+2, find the opposite of each term.

$$4\left(292x-x-2\right)\geq 33\left(x+1\right)$$

Combine 292x and -x to get 291x.

$$4\left(291x-2\right)\geq 33\left(x+1\right)$$

Use the distributive property to multiply 4 by 291x-2.

$$1164x-8\geq 33\left(x+1\right)$$

Use the distributive property to multiply 33 by x+1.

$$1164x-8\geq 33x+33$$

Subtract 33x from both sides.

$$1164x-8-33x\geq 33$$

Combine 1164x and -33x to get 1131x.

$$1131x-8\geq 33$$

Add 8 to both sides.

$$1131x\geq 33+8$$

Add 33 and 8 to get 41.

$$1131x\geq 41$$

Divide both sides by 1131. Since 1131 is positive, the inequality direction remains the same.

$$x\geq \frac{41}{1131}$$