Question

Write and solve the algebraic inequality.

The product of –3 and a number is at least -24.
A. -3x -24; x S 8
B. -3x -24; x 8
C. -3x <-24; x>-8
D. -3x >-24; x>-8

Answer 1

To write and solve the algebraic inequality, we can use the following steps: Let x represent the number, translate the given phrase into an inequality (-3x >= -24), multiply both sides by -1, divide both sides by 3, and the final inequality is x <= 8.

Step-by-step explanation:

To write and solve the algebraic inequality, we can use the following steps:

1. Let x represent the number that we are trying to find.
2. Translate the given phrase into an inequality. The product of -3 and a number is at least -24 can be written as -3x ≥ -24.
3. Multiply both sides of the inequality by -1 to change the sign. This gives us 3x ≤ 24.
4. Divide both sides of the inequality by 3 to isolate x. The final inequality is x ≤ 8.

Therefore, the correct answer is A. -3x - 24; x ≤ 8.

Answer 2

Step-by-step explanation:

Lets convert each sentence into an algebric inequality.

• Product of -3 and a number (let it be x) :-

`= > - 3 * x = - 3x`

• -3x is atleast -24

`= > - 3x \geqslant - 24`

Lets solve the inequality.

Now , divide -3 on both the sides -

`= > ( - 3x)/(-3) \geqslant ( - 24)/( - 3)`

`= > x \geqslant 8`