Solve (3x-1)(10x+4)geq(6x-5)(5x-7)

$$( 3 x - 1 ) ( 10 x + 4 ) \geq ( 6 x - 5 ) ( 5 x - 7 )$$

Solve for x

$$x\geq \frac{13}{23}$$

Solution Steps

Use the distributive property to multiply 3x-1 by 10x+4 and combine like terms.

$$30x^{2}+2x-4\geq \left(6x-5\right)\left(5x-7\right)$$

Use the distributive property to multiply 6x-5 by 5x-7 and combine like terms.

$$30x^{2}+2x-4\geq 30x^{2}-67x+35$$

Subtract 30x^{2} from both sides.

$$30x^{2}+2x-4-30x^{2}\geq -67x+35$$

Combine 30x^{2} and -30x^{2} to get 0.

$$2x-4\geq -67x+35$$

Add 67x to both sides.

$$2x-4+67x\geq 35$$

Combine 2x and 67x to get 69x.

$$69x-4\geq 35$$

Add 4 to both sides.

$$69x\geq 35+4$$

Add 35 and 4 to get 39.

$$69x\geq 39$$

Divide both sides by 69. Since 69 is positive, the inequality direction remains the same.

$$x\geq \frac{39}{69}$$

Reduce the fraction \frac{39}{69} to lowest terms by extracting and canceling out 3.

$$x\geq \frac{13}{23}$$