QuestionSolve the inequality $4|t+3| \geq 8$ .

Studdy Solution

STEP 1

Assumptions1. The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, it is always non-negative. . The inequality $4|t+3| \geq8$ is given.

STEP 2

First, we need to isolate the absolute value term. We can do this by dividing both sides of the inequality by4.
$|t+| \geq \frac{8}{4}$

STEP 3

implify the right side of the inequality.
$|t+3| \geq2$

STEP 4

The absolute value inequality $|t+3| \geq2$ can be rewritten as two separate inequalities $t+3 \geq2$ and $t+3 \leq -2$ .

STEP 5

Now, we can solve the first inequality $t+3 \geq2$ by subtracting3 from both sides.
$t \geq2 -3$

STEP 6

implify the right side of the inequality.
$t \geq -1$

STEP 7

Next, we can solve the second inequality $t+3 \leq -2$ by subtracting3 from both sides.
$t \leq -2 -3$

STEP 8

implify the right side of the inequality.
$t \leq -5$ So, the solution to the inequality $4|t+3| \geq8$ is $t \geq -1$ and $t \leq -5$ .

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QuestionSolve the inequality $4|t+3| \geq 8$ .

Studdy Solution

STEP 1

Assumptions1. The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, it is always non-negative. . The inequality $4|t+3| \geq8$ is given.

STEP 2

First, we need to isolate the absolute value term. We can do this by dividing both sides of the inequality by4.
$|t+| \geq \frac{8}{4}$

STEP 3

implify the right side of the inequality.
$|t+3| \geq2$

STEP 4

The absolute value inequality $|t+3| \geq2$ can be rewritten as two separate inequalities $t+3 \geq2$ and $t+3 \leq -2$ .

STEP 5

Now, we can solve the first inequality $t+3 \geq2$ by subtracting3 from both sides.
$t \geq2 -3$

STEP 6

implify the right side of the inequality.
$t \geq -1$

STEP 7

Next, we can solve the second inequality $t+3 \leq -2$ by subtracting3 from both sides.
$t \leq -2 -3$

STEP 8

implify the right side of the inequality.
$t \leq -5$ So, the solution to the inequality $4|t+3| \geq8$ is $t \geq -1$ and $t \leq -5$ .

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QuestionSolve the inequality 4∣t+3∣≥84|t+3| \geq 84∣t+3∣≥8.

Studdy Solution

STEP 1

Assumptions1. The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, it is always non-negative. . The inequality 4∣t+3∣≥84|t+3| \geq84∣t+3∣≥8 is given.

STEP 2

First, we need to isolate the absolute value term. We can do this by dividing both sides of the inequality by4.∣t+∣≥84|t+| \geq \frac{8}{4}∣t+∣≥48​

STEP 3

implify the right side of the inequality.∣t+3∣≥2|t+3| \geq2∣t+3∣≥2

STEP 4

The absolute value inequality ∣t+3∣≥2|t+3| \geq2∣t+3∣≥2 can be rewritten as two separate inequalities t+3≥2t+3 \geq2t+3≥2 and t+3≤−2t+3 \leq -2t+3≤−2.

STEP 5

Now, we can solve the first inequality t+3≥2t+3 \geq2t+3≥2 by subtracting3 from both sides.t≥2−3t \geq2 -3t≥2−3

STEP 6

implify the right side of the inequality.t≥−1t \geq -1t≥−1

STEP 7

Next, we can solve the second inequality t+3≤−2t+3 \leq -2t+3≤−2 by subtracting3 from both sides.t≤−2−3t \leq -2 -3t≤−2−3

STEP 8

implify the right side of the inequality.t≤−5t \leq -5t≤−5So, the solution to the inequality 4∣t+3∣≥84|t+3| \geq84∣t+3∣≥8 is t≥−1t \geq -1t≥−1 and t≤−5t \leq -5t≤−5.

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QuestionSolve the inequality $4|t+3| \geq 8$ .

Assumptions1. The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, it is always non-negative. . The inequality $4|t+3| \geq8$ is given.

First, we need to isolate the absolute value term. We can do this by dividing both sides of the inequality by4.
$|t+| \geq \frac{8}{4}$

implify the right side of the inequality.
$|t+3| \geq2$

The absolute value inequality $|t+3| \geq2$ can be rewritten as two separate inequalities $t+3 \geq2$ and $t+3 \leq -2$ .

Now, we can solve the first inequality $t+3 \geq2$ by subtracting3 from both sides.
$t \geq2 -3$

implify the right side of the inequality.
$t \geq -1$

Next, we can solve the second inequality $t+3 \leq -2$ by subtracting3 from both sides.
$t \leq -2 -3$

implify the right side of the inequality.
$t \leq -5$ So, the solution to the inequality $4|t+3| \geq8$ is $t \geq -1$ and $t \leq -5$ .