Math

Question Solve the system of linear inequalities: 12t20<2t12t - 20 < 2t, t<2t < 2, t>2t > 2, t>2t > -2, t<2t < -2.

Studdy Solution

STEP 1

Assumptions
1. We are given the inequality 12t20<2t12t - 20 < 2t.
2. We need to solve for the variable tt.

STEP 2

To isolate the variable tt on one side of the inequality, we first subtract 2t2t from both sides of the inequality.
12t202t<2t2t12t - 20 - 2t < 2t - 2t

STEP 3

Simplify both sides of the inequality by combining like terms.
10t20<010t - 20 < 0

STEP 4

Next, we add 2020 to both sides of the inequality to move the constant term to the right side.
10t20+20<0+2010t - 20 + 20 < 0 + 20

STEP 5

Simplify both sides of the inequality.
10t<2010t < 20

STEP 6

Now, we divide both sides of the inequality by 1010 to solve for tt.
10t10<2010\frac{10t}{10} < \frac{20}{10}

STEP 7

Simplify both sides of the inequality.
t<2t < 2
The solution to the inequality 12t20<2t12t - 20 < 2t is t<2t < 2.

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