Solve 3^2-[4*(a-1)*(-2)]geq0

$$3 ^ { 2 } - [ 4 \times ( a - 1 ) \times ( - 2 ) ] \geq 0$$

Solve for a

$$a\geq -\frac{1}{8}$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$9-4\left(a-1\right)\left(-2\right)\geq 0$$

Multiply 4 and -2 to get -8.

$$9-\left(-8\left(a-1\right)\right)\geq 0$$

The opposite of -8\left(a-1\right) is 8\left(a-1\right).

$$9+8\left(a-1\right)\geq 0$$

Use the distributive property to multiply 8 by a-1.

$$9+8a-8\geq 0$$

Subtract 8 from 9 to get 1.

$$1+8a\geq 0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$8a\geq -1$$

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

$$a\geq -\frac{1}{8}$$