Solve 3(x-4)geq7-5(x+1)

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

Solve for x

$$x\geq \frac{7}{4}$$

Solution Steps

Use the distributive property to multiply 3 by x-4.

$$3x-12\geq 7-5\left(x+1\right)$$

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

$$3x-12\geq 7-5x-5$$

Subtract 5 from 7 to get 2.

$$3x-12\geq 2-5x$$

Add 5x to both sides.

$$3x-12+5x\geq 2$$

Combine 3x and 5x to get 8x.

$$8x-12\geq 2$$

Add 12 to both sides.

$$8x\geq 2+12$$

Add 2 and 12 to get 14.

$$8x\geq 14$$

Divide both sides by 8. Since 8 is positive, the inequality direction remains the same.

$$x\geq \frac{14}{8}$$

Reduce the fraction \frac{14}{8} to lowest terms by extracting and canceling out 2.

$$x\geq \frac{7}{4}$$