QuestionSimplify the expression: $-2(4 x+3)+(3 y+3)$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $-(4 x+3)+(3 y+3)$ . We need to simplify this expression

STEP 2

We begin by applying the distributive property (also known as the distributive law), which states that for all real numbers a, b, and c a(b + c) = ab + ac. We apply this to the first term in the expression.
$-2(4x +) = -2 \cdot4x + -2 \cdot$

STEP 3

Now, we simplify the multiplication in the expression.
-2 \cdotx + -2 \cdot3 = -8x -6

STEP 4

Next, we apply the distributive property to the second term in the expression.
$(3y +3) =3 \cdot y +3 \cdot1$

STEP 5

We simplify the multiplication in the expression.
$3 \cdot y +3 \cdot1 =3y +3$

STEP 6

Finally, we combine the simplified expressions from steps3 and5 to get the simplified form of the original expression.
$-8x -6 +3y +3$

STEP 7

We simplify the expression by combining like terms.
$-x +3y -6 +3 = -x +3y -3$ The simplified form of the given expression is $-x +3y -3$ .

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QuestionSimplify the expression: $-2(4 x+3)+(3 y+3)$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $-(4 x+3)+(3 y+3)$ . We need to simplify this expression

STEP 2

We begin by applying the distributive property (also known as the distributive law), which states that for all real numbers a, b, and c a(b + c) = ab + ac. We apply this to the first term in the expression.
$-2(4x +) = -2 \cdot4x + -2 \cdot$

STEP 3

Now, we simplify the multiplication in the expression.
-2 \cdotx + -2 \cdot3 = -8x -6

STEP 4

Next, we apply the distributive property to the second term in the expression.
$(3y +3) =3 \cdot y +3 \cdot1$

STEP 5

We simplify the multiplication in the expression.
$3 \cdot y +3 \cdot1 =3y +3$

STEP 6

Finally, we combine the simplified expressions from steps3 and5 to get the simplified form of the original expression.
$-8x -6 +3y +3$

STEP 7

We simplify the expression by combining like terms.
$-x +3y -6 +3 = -x +3y -3$ The simplified form of the given expression is $-x +3y -3$ .

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QuestionSimplify the expression: −2(4x+3)+(3y+3)-2(4 x+3)+(3 y+3)−2(4x+3)+(3y+3).

Studdy Solution

STEP 1

Assumptions1. We are given the expression −(4x+3)+(3y+3)-(4 x+3)+(3 y+3)−(4x+3)+(3y+3). We need to simplify this expression

STEP 2

We begin by applying the distributive property (also known as the distributive law), which states that for all real numbers a, b, and c a(b + c) = ab + ac. We apply this to the first term in the expression.−2(4x+)=−2⋅4x+−2⋅-2(4x +) = -2 \cdot4x + -2 \cdot−2(4x+)=−2⋅4x+−2⋅

STEP 3

Now, we simplify the multiplication in the expression.-2 \cdotx + -2 \cdot3 = -8x -6

STEP 4

Next, we apply the distributive property to the second term in the expression.(3y+3)=3⋅y+3⋅1(3y +3) =3 \cdot y +3 \cdot1(3y+3)=3⋅y+3⋅1

STEP 5

We simplify the multiplication in the expression.3⋅y+3⋅1=3y+33 \cdot y +3 \cdot1 =3y +33⋅y+3⋅1=3y+3

STEP 6

Finally, we combine the simplified expressions from steps3 and5 to get the simplified form of the original expression.−8x−6+3y+3-8x -6 +3y +3−8x−6+3y+3

STEP 7

We simplify the expression by combining like terms.−x+3y−6+3=−x+3y−3-x +3y -6 +3 = -x +3y -3−x+3y−6+3=−x+3y−3The simplified form of the given expression is −x+3y−3-x +3y -3−x+3y−3.

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QuestionSimplify the expression: $-2(4 x+3)+(3 y+3)$ .

Assumptions1. We are given the expression $-(4 x+3)+(3 y+3)$ . We need to simplify this expression

We begin by applying the distributive property (also known as the distributive law), which states that for all real numbers a, b, and c a(b + c) = ab + ac. We apply this to the first term in the expression.
$-2(4x +) = -2 \cdot4x + -2 \cdot$

Now, we simplify the multiplication in the expression.
-2 \cdotx + -2 \cdot3 = -8x -6

Next, we apply the distributive property to the second term in the expression.
$(3y +3) =3 \cdot y +3 \cdot1$

We simplify the multiplication in the expression.
$3 \cdot y +3 \cdot1 =3y +3$

Finally, we combine the simplified expressions from steps3 and5 to get the simplified form of the original expression.
$-8x -6 +3y +3$

We simplify the expression by combining like terms.
$-x +3y -6 +3 = -x +3y -3$ The simplified form of the given expression is $-x +3y -3$ .