Solve 5(2x-6)+4<4-2(x-6)

$$5 ( 2 x - 6 ) + 4 < 4 - 2 ( x - 6 )$$

Solve for x

$$x<\frac{7}{2}$$

Solution Steps

Use the distributive property to multiply 5 by 2x-6.

$$10x-30+4<4-2\left(x-6\right)$$

Add -30 and 4 to get -26.

$$10x-26<4-2\left(x-6\right)$$

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

$$10x-26<4-2x+12$$

Add 4 and 12 to get 16.

$$10x-26<16-2x$$

Add 2x to both sides.

$$10x-26+2x<16$$

Combine 10x and 2x to get 12x.

$$12x-26<16$$

Add 26 to both sides.

$$12x<16+26$$

Add 16 and 26 to get 42.

$$12x<42$$

Divide both sides by 12. Since 12 is positive, the inequality direction remains the same.

$$x<\frac{42}{12}$$

Reduce the fraction \frac{42}{12} to lowest terms by extracting and canceling out 6.

$$x<\frac{7}{2}$$