Solve (9x+46)(x+3)leq(3x+19)(3x+10)

$$( 9 x + 46 ) ( x + 3 ) \leq ( 3 x + 19 ) ( 3 x + 10 )$$

Solve for x

$$x\geq -\frac{26}{7}$$

Solution Steps

Use the distributive property to multiply 9x+46 by x+3 and combine like terms.

$$9x^{2}+73x+138\leq \left(3x+19\right)\left(3x+10\right)$$

Use the distributive property to multiply 3x+19 by 3x+10 and combine like terms.

$$9x^{2}+73x+138\leq 9x^{2}+87x+190$$

Subtract 9x^{2} from both sides.

$$9x^{2}+73x+138-9x^{2}\leq 87x+190$$

Combine 9x^{2} and -9x^{2} to get 0.

$$73x+138\leq 87x+190$$

Subtract 87x from both sides.

$$73x+138-87x\leq 190$$

Combine 73x and -87x to get -14x.

$$-14x+138\leq 190$$

Subtract 138 from both sides.

$$-14x\leq 190-138$$

Subtract 138 from 190 to get 52.

$$-14x\leq 52$$

Divide both sides by -14. Since -14 is negative, the inequality direction is changed.

$$x\geq \frac{52}{-14}$$

Reduce the fraction \frac{52}{-14} to lowest terms by extracting and canceling out 2.

$$x\geq -\frac{26}{7}$$