You are here:

- Home
- Science
- Math for Kids
- Algebra
- Alg2 solving inequalities and absolute values

Advertisement

2 |9t-3| + 4t ≤ 12

To solve 2|9t-3| + 4t ≤ 12, what matters is whether 9t-3 is positive or negative.

If 9t-3 is positive, the equation is 2(9t-3) + 4t ≤ 12.

If 9t-3 is negative, the equation is 2(-9t+3) + 4t ≤ 12.

For 9t-3 to be positive, solve 9t-3 >= 0.

That is the same as 9t >= 3, so we need t >= 3/9, which is t >= 1/3.

In this case, our equation is 2(9t-3) + 4t ≤ 12.

This is the same as 18t - 6 + 4t ≤ 12. Noting that 18t + 4t is 22t and adding 6 to both sides gives 22t <= 18, so t <= 18/22 => t <= 9/11.

This implies we need 1/3 <= t <= 9/11.

For 9t-3 being negative, this means 9t-3 < 0 => 9t < 3 => t < 1/3.

In this case, the equation to solve is 2(-9t+3) + 4t ≤ 12.

That multiplies into -18t + 6 + 4t ≤ 12.

Combining the t terms and subtracting 6 from both sides gives -14t ≤6.

We need to multiply both sides by -1/14, and since it is negative,

it changes the sign to a greater than or equal to.

That gives t >= 6/14 => t >= 3/7.

Since we need both t to be less than a third and greater than 3/7, this is not possible.

Algebra

Answers by Expert:

Any algebraic question you've got. That includes question that are linear, quadratic, exponential, etc.

I have solved story problems, linear equations, parabolic equations.
I have also solved some 3rd order equations and equations with multiple variables.
**Publications**

Documents at Boeing in assistance on the manufacturiing floor.**Education/Credentials**

MS at math OSU in mathematics at OSU, 1986.
BS at OSU in mathematical sciences (math, statistics, computer science), 1984.
**Awards and Honors**

Both my BS and MS degrees were given with honors.
**Past/Present Clients**

Students in a wide variety of areas since the 80's; over 1,000 of them have been in algebra.