Question Solve the equation $3(16-3x)=-6$ using properties of equality. Options are (A) $x=-8$ , (B) $x=-6$ , (C) $x=6$ , (D) $x=-9$ .

Studdy Solution

STEP 1

Assumptions
1. We are solving the equation for the variable $x$ .
2. We are using properties of equality to solve the equation.
3. The equation is $3(16-3x)=-6$ .

STEP 2

First, we distribute the $3$ to both terms inside the parentheses.
$3(16-3x) = 316 - 33x = 48 - 9x$
So, the equation becomes:
$48 - 9x = -6$

STEP 3

Next, we isolate the term with $x$ on one side of the equation by subtracting $48$ from both sides.
$48 - 9x - 48 = -6 - 48$
This simplifies to:
$-9x = -54$

STEP 4

Finally, we solve for $x$ by dividing both sides of the equation by $-9$ .
$x = -54 / -9$

STEP 5

Calculate the value of $x$ .
$x = -54 / -9 = 6$
So, the solution to the equation is $x=6$ .

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Question Solve the equation $3(16-3x)=-6$ using properties of equality. Options are (A) $x=-8$ , (B) $x=-6$ , (C) $x=6$ , (D) $x=-9$ .

Studdy Solution

STEP 1

Assumptions
1. We are solving the equation for the variable $x$ .
2. We are using properties of equality to solve the equation.
3. The equation is $3(16-3x)=-6$ .

STEP 2

First, we distribute the $3$ to both terms inside the parentheses.
$3(16-3x) = 316 - 33x = 48 - 9x$
So, the equation becomes:
$48 - 9x = -6$

STEP 3

Next, we isolate the term with $x$ on one side of the equation by subtracting $48$ from both sides.
$48 - 9x - 48 = -6 - 48$
This simplifies to:
$-9x = -54$

STEP 4

Finally, we solve for $x$ by dividing both sides of the equation by $-9$ .
$x = -54 / -9$

STEP 5

Calculate the value of $x$ .
$x = -54 / -9 = 6$
So, the solution to the equation is $x=6$ .

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Question Solve the equation 3(16−3x)=−63(16-3x)=-63(16−3x)=−6 using properties of equality. Options are (A) x=−8x=-8x=−8, (B) x=−6x=-6x=−6, (C) x=6x=6x=6, (D) x=−9x=-9x=−9.

Studdy Solution

STEP 1

Assumptions1. We are solving the equation for the variable xxx.2. We are using properties of equality to solve the equation.3. The equation is 3(16−3x)=−63(16-3x)=-63(16−3x)=−6.

STEP 2

First, we distribute the 333 to both terms inside the parentheses.3(16−3x)=3∗16−3∗3x=48−9x3(16-3x) = 3*16 - 3*3x = 48 - 9x3(16−3x)=3∗16−3∗3x=48−9xSo, the equation becomes:48−9x=−648 - 9x = -648−9x=−6

STEP 3

Next, we isolate the term with xxx on one side of the equation by subtracting 484848 from both sides.48−9x−48=−6−4848 - 9x - 48 = -6 - 4848−9x−48=−6−48This simplifies to:−9x=−54-9x = -54−9x=−54

STEP 4

Finally, we solve for xxx by dividing both sides of the equation by −9-9−9.x=−54/−9x = -54 / -9x=−54/−9

STEP 5

Calculate the value of xxx.x=−54/−9=6x = -54 / -9 = 6x=−54/−9=6So, the solution to the equation is x=6x=6x=6.

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Question Solve the equation $3(16-3x)=-6$ using properties of equality. Options are (A) $x=-8$ , (B) $x=-6$ , (C) $x=6$ , (D) $x=-9$ .

Assumptions
1. We are solving the equation for the variable $x$ .
2. We are using properties of equality to solve the equation.
3. The equation is $3(16-3x)=-6$ .

First, we distribute the $3$ to both terms inside the parentheses.
$3(16-3x) = 316 - 33x = 48 - 9x$
So, the equation becomes:
$48 - 9x = -6$

Next, we isolate the term with $x$ on one side of the equation by subtracting $48$ from both sides.
$48 - 9x - 48 = -6 - 48$
This simplifies to:
$-9x = -54$

Finally, we solve for $x$ by dividing both sides of the equation by $-9$ .
$x = -54 / -9$

Calculate the value of $x$ .
$x = -54 / -9 = 6$
So, the solution to the equation is $x=6$ .