Question Solve the inequality $3(3-x)<12$ for the value of $x$ .

Studdy Solution

STEP 1

Assumptions1. We are given the inequality $3(3-x)<12$ . . We need to solve this inequality for $x$ .

STEP 2

First, we distribute the $$ on the left side of the inequality.
$(-x) =* -*x$

STEP 3

Calculate the multiplication to simplify the left side of the inequality.
$33 -3x =9 -3x$

STEP 4

Now, we replace the left side of the inequality with the simplified expression.
$9 -3x <12$

STEP 5

Next, we isolate $-3x$ on the left side of the inequality by subtracting $9$ from both sides.
$9 -3x -9 <12 -9$

STEP 6

implify both sides of the inequality.
$-3x <3$

STEP 7

Now, we isolate $x$ on the left side of the inequality by dividing both sides by $-3$ . Remember, when we divide or multiply both sides of an inequality by a negative number, the direction of the inequality sign changes.
$x > -1$ So, the solution to the inequality $3(3-x)<12$ is $x > -1$ .

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Question Solve the inequality $3(3-x)<12$ for the value of $x$ .

Studdy Solution

STEP 1

Assumptions1. We are given the inequality $3(3-x)<12$ . . We need to solve this inequality for $x$ .

STEP 2

First, we distribute the $$ on the left side of the inequality.
$(-x) =* -*x$

STEP 3

Calculate the multiplication to simplify the left side of the inequality.
$33 -3x =9 -3x$

STEP 4

Now, we replace the left side of the inequality with the simplified expression.
$9 -3x <12$

STEP 5

Next, we isolate $-3x$ on the left side of the inequality by subtracting $9$ from both sides.
$9 -3x -9 <12 -9$

STEP 6

implify both sides of the inequality.
$-3x <3$

STEP 7

Now, we isolate $x$ on the left side of the inequality by dividing both sides by $-3$ . Remember, when we divide or multiply both sides of an inequality by a negative number, the direction of the inequality sign changes.
$x > -1$ So, the solution to the inequality $3(3-x)<12$ is $x > -1$ .

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Question Solve the inequality 3(3−x)<123(3-x)<123(3−x)<12 for the value of xxx.

Studdy Solution

STEP 1

Assumptions1. We are given the inequality 3(3−x)<123(3-x)<123(3−x)<12. . We need to solve this inequality for xxx.

STEP 2

First, we distribute the $$ on the left side of the inequality.(−x)=∗−∗x(-x) =* -*x(−x)=∗−∗x

STEP 3

Calculate the multiplication to simplify the left side of the inequality.3∗3−3∗x=9−3x3*3 -3*x =9 -3x3∗3−3∗x=9−3x

STEP 4

Now, we replace the left side of the inequality with the simplified expression.9−3x<129 -3x <129−3x<12

STEP 5

Next, we isolate −3x-3x−3x on the left side of the inequality by subtracting 999 from both sides.9−3x−9<12−99 -3x -9 <12 -99−3x−9<12−9

STEP 6

implify both sides of the inequality.−3x<3-3x <3−3x<3

STEP 7

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Question Solve the inequality $3(3-x)<12$ for the value of $x$ .

Assumptions1. We are given the inequality $3(3-x)<12$ . . We need to solve this inequality for $x$ .

First, we distribute the $$ on the left side of the inequality.
$(-x) =* -*x$

Calculate the multiplication to simplify the left side of the inequality.
$33 -3x =9 -3x$

Now, we replace the left side of the inequality with the simplified expression.
$9 -3x <12$

Next, we isolate $-3x$ on the left side of the inequality by subtracting $9$ from both sides.
$9 -3x -9 <12 -9$

implify both sides of the inequality.
$-3x <3$