Question Simplify the expression $2(-12x - \frac{3}{2}) + 4x$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the expression $2(-12x - \frac{3}{2}) + 4x$ .
2. We need to simplify the expression by distributing and combining like terms.

STEP 2

First, distribute the 2 across the terms inside the parentheses.
$2(-12x - \frac{3}{2}) = 2 \cdot (-12x) + 2 \cdot (-\frac{3}{2})$

STEP 3

Multiply $2$ by $-12x$ .
$2 \cdot (-12x) = -24x$

STEP 4

Multiply $2$ by $-\frac{3}{2}$ .
$2 \cdot (-\frac{3}{2}) = -3$

STEP 5

Now, rewrite the expression with the distributed terms.
$-24x - 3 + 4x$

STEP 6

Combine like terms, which are the terms with the variable $x$ .
$-24x + 4x = -20x$

STEP 7

The final simplified expression is the combination of the like terms and the constant term.
$-20x - 3$
The simplified form of the expression $2(-12x - \frac{3}{2}) + 4x$ is $-20x - 3$ .

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Question Simplify the expression $2(-12x - \frac{3}{2}) + 4x$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the expression $2(-12x - \frac{3}{2}) + 4x$ .
2. We need to simplify the expression by distributing and combining like terms.

STEP 2

First, distribute the 2 across the terms inside the parentheses.
$2(-12x - \frac{3}{2}) = 2 \cdot (-12x) + 2 \cdot (-\frac{3}{2})$

STEP 3

Multiply $2$ by $-12x$ .
$2 \cdot (-12x) = -24x$

STEP 4

Multiply $2$ by $-\frac{3}{2}$ .
$2 \cdot (-\frac{3}{2}) = -3$

STEP 5

Now, rewrite the expression with the distributed terms.
$-24x - 3 + 4x$

STEP 6

Combine like terms, which are the terms with the variable $x$ .
$-24x + 4x = -20x$

STEP 7

The final simplified expression is the combination of the like terms and the constant term.
$-20x - 3$
The simplified form of the expression $2(-12x - \frac{3}{2}) + 4x$ is $-20x - 3$ .

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Question Simplify the expression 2(−12x−32)+4x2(-12x - \frac{3}{2}) + 4x2(−12x−23​)+4x.

Studdy Solution

STEP 1

Assumptions1. We are given the expression 2(−12x−32)+4x2(-12x - \frac{3}{2}) + 4x2(−12x−23​)+4x.2. We need to simplify the expression by distributing and combining like terms.

STEP 2

First, distribute the 2 across the terms inside the parentheses.2(−12x−32)=2⋅(−12x)+2⋅(−32)2(-12x - \frac{3}{2}) = 2 \cdot (-12x) + 2 \cdot (-\frac{3}{2})2(−12x−23​)=2⋅(−12x)+2⋅(−23​)

STEP 3

Multiply 222 by −12x-12x−12x.2⋅(−12x)=−24x2 \cdot (-12x) = -24x2⋅(−12x)=−24x

STEP 4

Multiply 222 by −32-\frac{3}{2}−23​.2⋅(−32)=−32 \cdot (-\frac{3}{2}) = -32⋅(−23​)=−3

STEP 5

Now, rewrite the expression with the distributed terms.−24x−3+4x-24x - 3 + 4x−24x−3+4x

STEP 6

Combine like terms, which are the terms with the variable xxx.−24x+4x=−20x-24x + 4x = -20x−24x+4x=−20x

STEP 7

The final simplified expression is the combination of the like terms and the constant term.−20x−3-20x - 3−20x−3The simplified form of the expression 2(−12x−32)+4x2(-12x - \frac{3}{2}) + 4x2(−12x−23​)+4x is −20x−3-20x - 3−20x−3.

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Question Simplify the expression $2(-12x - \frac{3}{2}) + 4x$ .

Assumptions
1. We are given the expression $2(-12x - \frac{3}{2}) + 4x$ .
2. We need to simplify the expression by distributing and combining like terms.

First, distribute the 2 across the terms inside the parentheses.
$2(-12x - \frac{3}{2}) = 2 \cdot (-12x) + 2 \cdot (-\frac{3}{2})$

Multiply $2$ by $-12x$ .
$2 \cdot (-12x) = -24x$

Multiply $2$ by $-\frac{3}{2}$ .
$2 \cdot (-\frac{3}{2}) = -3$

Now, rewrite the expression with the distributed terms.
$-24x - 3 + 4x$

Combine like terms, which are the terms with the variable $x$ .
$-24x + 4x = -20x$

The final simplified expression is the combination of the like terms and the constant term.
$-20x - 3$
The simplified form of the expression $2(-12x - \frac{3}{2}) + 4x$ is $-20x - 3$ .