Question Simplify the expression $3y + 6x - 2(x + 5/2) + 6y$ .

Studdy Solution

STEP 1

1. The expression $(3 y+6 x)-2\left(x+\frac{5}{2}\right)+6 y$ involves real numbers and follows the standard rules of algebra.
2. The expression can be simplified by distributing, combining like terms, and applying arithmetic operations.

STEP 2

1. Distribute the negative sign and any coefficients across the terms within parentheses.
2. Combine like terms.
3. Simplify the expression to its most reduced form.

STEP 3

Distribute the negative sign and the coefficient $-2$ across the terms within the parentheses.
$(3 y+6 x)-2\left(x+\frac{5}{2}\right)+6 y = 3 y + 6 x - 2x - 2 \cdot \frac{5}{2} + 6 y$

STEP 4

Simplify the multiplication of $-2$ and $\frac{5}{2}$ .
$3 y + 6 x - 2x - 2 \cdot \frac{5}{2} + 6 y = 3 y + 6 x - 2x - 5 + 6 y$

STEP 5

Combine like terms, starting with the $y$ terms.
$3 y + 6 y = 9 y$

STEP 6

Combine like terms, now focusing on the $x$ terms.
$6 x - 2x = 4 x$

STEP 7

Combine the results from steps 3 and 4 and include the constant term.
$9 y + 4 x - 5$

STEP 8

The expression is now simplified to its most reduced form.
$(3 y+6 x)-2\left(x+\frac{5}{2}\right)+6 y = 9 y + 4 x - 5$
The simplified form of the expression is $9 y + 4 x - 5$ .

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Question Simplify the expression $3y + 6x - 2(x + 5/2) + 6y$ .

Studdy Solution

STEP 1

1. The expression $(3 y+6 x)-2\left(x+\frac{5}{2}\right)+6 y$ involves real numbers and follows the standard rules of algebra.
2. The expression can be simplified by distributing, combining like terms, and applying arithmetic operations.

STEP 2

1. Distribute the negative sign and any coefficients across the terms within parentheses.
2. Combine like terms.
3. Simplify the expression to its most reduced form.

STEP 3

Distribute the negative sign and the coefficient $-2$ across the terms within the parentheses.
$(3 y+6 x)-2\left(x+\frac{5}{2}\right)+6 y = 3 y + 6 x - 2x - 2 \cdot \frac{5}{2} + 6 y$

STEP 4

Simplify the multiplication of $-2$ and $\frac{5}{2}$ .
$3 y + 6 x - 2x - 2 \cdot \frac{5}{2} + 6 y = 3 y + 6 x - 2x - 5 + 6 y$

STEP 5

Combine like terms, starting with the $y$ terms.
$3 y + 6 y = 9 y$

STEP 6

Combine like terms, now focusing on the $x$ terms.
$6 x - 2x = 4 x$

STEP 7

Combine the results from steps 3 and 4 and include the constant term.
$9 y + 4 x - 5$

STEP 8

The expression is now simplified to its most reduced form.
$(3 y+6 x)-2\left(x+\frac{5}{2}\right)+6 y = 9 y + 4 x - 5$
The simplified form of the expression is $9 y + 4 x - 5$ .

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Question Simplify the expression 3y+6x−2(x+5/2)+6y3y + 6x - 2(x + 5/2) + 6y3y+6x−2(x+5/2)+6y.

Studdy Solution

STEP 1

1. The expression (3y+6x)−2(x+52)+6y(3 y+6 x)-2\left(x+\frac{5}{2}\right)+6 y(3y+6x)−2(x+25​)+6y involves real numbers and follows the standard rules of algebra.2. The expression can be simplified by distributing, combining like terms, and applying arithmetic operations.

STEP 2

1. Distribute the negative sign and any coefficients across the terms within parentheses.2. Combine like terms.3. Simplify the expression to its most reduced form.

STEP 3

Distribute the negative sign and the coefficient −2-2−2 across the terms within the parentheses.(3y+6x)−2(x+52)+6y=3y+6x−2x−2⋅52+6y (3 y+6 x)-2\left(x+\frac{5}{2}\right)+6 y = 3 y + 6 x - 2x - 2 \cdot \frac{5}{2} + 6 y (3y+6x)−2(x+25​)+6y=3y+6x−2x−2⋅25​+6y

STEP 4

Simplify the multiplication of −2-2−2 and 52\frac{5}{2}25​.3y+6x−2x−2⋅52+6y=3y+6x−2x−5+6y 3 y + 6 x - 2x - 2 \cdot \frac{5}{2} + 6 y = 3 y + 6 x - 2x - 5 + 6 y 3y+6x−2x−2⋅25​+6y=3y+6x−2x−5+6y

STEP 5

Combine like terms, starting with the yyy terms.3y+6y=9y 3 y + 6 y = 9 y 3y+6y=9y

STEP 6

Combine like terms, now focusing on the xxx terms.6x−2x=4x 6 x - 2x = 4 x 6x−2x=4x

STEP 7

Combine the results from steps 3 and 4 and include the constant term.9y+4x−5 9 y + 4 x - 5 9y+4x−5

STEP 8

The expression is now simplified to its most reduced form.(3y+6x)−2(x+52)+6y=9y+4x−5 (3 y+6 x)-2\left(x+\frac{5}{2}\right)+6 y = 9 y + 4 x - 5 (3y+6x)−2(x+25​)+6y=9y+4x−5The simplified form of the expression is 9y+4x−59 y + 4 x - 59y+4x−5.

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Question Simplify the expression $3y + 6x - 2(x + 5/2) + 6y$ .

1. The expression $(3 y+6 x)-2\left(x+\frac{5}{2}\right)+6 y$ involves real numbers and follows the standard rules of algebra.
2. The expression can be simplified by distributing, combining like terms, and applying arithmetic operations.

1. Distribute the negative sign and any coefficients across the terms within parentheses.
2. Combine like terms.
3. Simplify the expression to its most reduced form.

Distribute the negative sign and the coefficient $-2$ across the terms within the parentheses.
$(3 y+6 x)-2\left(x+\frac{5}{2}\right)+6 y = 3 y + 6 x - 2x - 2 \cdot \frac{5}{2} + 6 y$

Simplify the multiplication of $-2$ and $\frac{5}{2}$ .
$3 y + 6 x - 2x - 2 \cdot \frac{5}{2} + 6 y = 3 y + 6 x - 2x - 5 + 6 y$

Combine like terms, starting with the $y$ terms.
$3 y + 6 y = 9 y$

Combine like terms, now focusing on the $x$ terms.
$6 x - 2x = 4 x$

Combine the results from steps 3 and 4 and include the constant term.
$9 y + 4 x - 5$

The expression is now simplified to its most reduced form.
$(3 y+6 x)-2\left(x+\frac{5}{2}\right)+6 y = 9 y + 4 x - 5$
The simplified form of the expression is $9 y + 4 x - 5$ .