Solve 5*(2x-1)-6*(3-2x)geq1

$$5 \cdot ( 2 x - 1 ) - 6 \cdot ( 3 - 2 x ) \geq 1$$

Solve for x

$$x\geq \frac{12}{11}$$

Solution Steps

Use the distributive property to multiply 5 by 2x-1.

$$10x-5-6\left(3-2x\right)\geq 1$$

Use the distributive property to multiply -6 by 3-2x.

$$10x-5-18+12x\geq 1$$

Subtract 18 from -5 to get -23.

$$10x-23+12x\geq 1$$

Combine 10x and 12x to get 22x.

$$22x-23\geq 1$$

Add 23 to both sides.

$$22x\geq 1+23$$

Add 1 and 23 to get 24.

$$22x\geq 24$$

Divide both sides by 22. Since 22 is positive, the inequality direction remains the same.

$$x\geq \frac{24}{22}$$

Reduce the fraction \frac{24}{22} to lowest terms by extracting and canceling out 2.

$$x\geq \frac{12}{11}$$