Solve 3(2x+7)-9x+1geq2(5x-2)+3

$$3 ( 2 x + 7 ) - 9 x + 1 \geq 2 ( 5 x - 2 ) + 3$$

Solve for x

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

Solution Steps

Use the distributive property to multiply 3 by 2x+7.

$$6x+21-9x+1\geq 2\left(5x-2\right)+3$$

Combine 6x and -9x to get -3x.

$$-3x+21+1\geq 2\left(5x-2\right)+3$$

Add 21 and 1 to get 22.

$$-3x+22\geq 2\left(5x-2\right)+3$$

Use the distributive property to multiply 2 by 5x-2.

$$-3x+22\geq 10x-4+3$$

Add -4 and 3 to get -1.

$$-3x+22\geq 10x-1$$

Subtract 10x from both sides.

$$-3x+22-10x\geq -1$$

Combine -3x and -10x to get -13x.

$$-13x+22\geq -1$$

Subtract 22 from both sides.

$$-13x\geq -1-22$$

Subtract 22 from -1 to get -23.

$$-13x\geq -23$$

Divide both sides by -13. Since -13 is negative, the inequality direction is changed.

$$x\leq \frac{-23}{-13}$$

Fraction \frac{-23}{-13} can be simplified to \frac{23}{13} by removing the negative sign from both the numerator and the denominator.

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