Solved on Sep 15, 2023

Solve for $t$ where $|t+4|=11$ . Express the solution(s) as integers or simplified fractions.

STEP 1

Assumptions1. The equation is $|t+4|=11$ . The absolute value of a number is its distance from zero on the number line, which is always positive or zero.
3. We are solving for the variable $t$ .

STEP 2

The absolute value equation $|t+4|=11$ can be broken down into two separate equations. This is because the expression inside the absolute value, $t+4$ , can be either positive or negative, and still yield a positive result after taking the absolute value.
So, we write $t+4=11$ or $t+4=-11$

STEP 3

olve the first equation $t+=11$ for $t$ by subtracting from both sides.
$t+-=11-$

STEP 4

implify the equation to find the value of $t$ .
$t=11-4=7$

STEP 5

Now, solve the second equation $t+4=-11$ for $t$ by subtracting4 from both sides.
$t+4-4=-11-4$

STEP 6

implify the equation to find the value of $t$ .
$t=-11-4=-15$ So, the solutions to the equation $|t+4|=11$ are $t=$ and $t=-15$ .

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Solve for $t$ where $|t+4|=11$ . Express the solution(s) as integers or simplified fractions.

STEP 1

Assumptions1. The equation is $|t+4|=11$ . The absolute value of a number is its distance from zero on the number line, which is always positive or zero.
3. We are solving for the variable $t$ .

STEP 2

The absolute value equation $|t+4|=11$ can be broken down into two separate equations. This is because the expression inside the absolute value, $t+4$ , can be either positive or negative, and still yield a positive result after taking the absolute value.
So, we write $t+4=11$ or $t+4=-11$

STEP 3

olve the first equation $t+=11$ for $t$ by subtracting from both sides.
$t+-=11-$

STEP 4

implify the equation to find the value of $t$ .
$t=11-4=7$

STEP 5

Now, solve the second equation $t+4=-11$ for $t$ by subtracting4 from both sides.
$t+4-4=-11-4$

STEP 6

implify the equation to find the value of $t$ .
$t=-11-4=-15$ So, the solutions to the equation $|t+4|=11$ are $t=$ and $t=-15$ .

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Solve for ttt where ∣t+4∣=11|t+4|=11∣t+4∣=11. Express the solution(s) as integers or simplified fractions.

STEP 1

Assumptions1. The equation is ∣t+4∣=11|t+4|=11∣t+4∣=11 . The absolute value of a number is its distance from zero on the number line, which is always positive or zero.3. We are solving for the variable ttt.

STEP 2

STEP 3

olve the first equation t+=11t+=11t+=11 for ttt by subtracting from both sides.t+−=11−t+-=11-t+−=11−

STEP 4

implify the equation to find the value of ttt.t=11−4=7t=11-4=7t=11−4=7

STEP 5

Now, solve the second equation t+4=−11t+4=-11t+4=−11 for ttt by subtracting4 from both sides.t+4−4=−11−4t+4-4=-11-4t+4−4=−11−4

STEP 6

implify the equation to find the value of ttt.t=−11−4=−15t=-11-4=-15t=−11−4=−15So, the solutions to the equation ∣t+4∣=11|t+4|=11∣t+4∣=11 are t=t=t= and t=−15t=-15t=−15.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Solve for $t$ where $|t+4|=11$ . Express the solution(s) as integers or simplified fractions.

Assumptions1. The equation is $|t+4|=11$ . The absolute value of a number is its distance from zero on the number line, which is always positive or zero.
3. We are solving for the variable $t$ .

olve the first equation $t+=11$ for $t$ by subtracting from both sides.
$t+-=11-$

implify the equation to find the value of $t$ .
$t=11-4=7$

Now, solve the second equation $t+4=-11$ for $t$ by subtracting4 from both sides.
$t+4-4=-11-4$

implify the equation to find the value of $t$ .
$t=-11-4=-15$ So, the solutions to the equation $|t+4|=11$ are $t=$ and $t=-15$ .