Solve 7(1-x)geq3(2+3x)

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

Solve for x

$$x\leq \frac{1}{16}$$

Solution Steps

Use the distributive property to multiply 7 by 1-x.

$$7-7x\geq 3\left(2+3x\right)$$

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

$$7-7x\geq 6+9x$$

Subtract 9x from both sides.

$$7-7x-9x\geq 6$$

Combine -7x and -9x to get -16x.

$$7-16x\geq 6$$

Subtract 7 from both sides.

$$-16x\geq 6-7$$

Subtract 7 from 6 to get -1.

$$-16x\geq -1$$

Divide both sides by -16. Since -16 is negative, the inequality direction is changed.

$$x\leq \frac{-1}{-16}$$

Fraction \frac{-1}{-16} can be simplified to \frac{1}{16} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{1}{16}$$