QuestionFind the equivalent expression for $\frac{1}{6}(30 x-24 y)-\frac{1}{8}(32 x-16 y)$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $\frac{1}{6}(30 x-24 y)-\frac{1}{8}(32 x-16 y)$ . We need to simplify this expression to its equivalent form

STEP 2

First, we distribute the fractions in each term. $\frac{1}{6}(30 x-24 y) = \frac{1}{6} \cdot30x - \frac{1}{6} \cdot24y$ $\frac{1}{8}(32 x-16 y) = \frac{1}{8} \cdot32x - \frac{1}{8} \cdot16y$

STEP 3

Now, simplify the multiplication in each term.
$\frac{1}{6} \cdot30x =5x$ $\frac{1}{6} \cdot24y =y$ $\frac{1}{8} \cdot32x =x$ $\frac{1}{8} \cdot16y =2y$

STEP 4

Substitute these simplified terms back into the original expression.
$\frac{1}{6}(30 x-24 y)-\frac{1}{8}(32 x-16 y) =x -4y -4x +2y$

STEP 5

Combine like terms.
$5x -4x = x$ $-4y +2y = -2y$

STEP 6

Write the final simplified expression.
$x -2y$ The expression $\frac{1}{6}(30 x-24 y)-\frac{1}{8}(32 x-16 y)$ is equivalent to $x -2y$ .

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QuestionFind the equivalent expression for $\frac{1}{6}(30 x-24 y)-\frac{1}{8}(32 x-16 y)$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $\frac{1}{6}(30 x-24 y)-\frac{1}{8}(32 x-16 y)$ . We need to simplify this expression to its equivalent form

STEP 2

First, we distribute the fractions in each term. $\frac{1}{6}(30 x-24 y) = \frac{1}{6} \cdot30x - \frac{1}{6} \cdot24y$ $\frac{1}{8}(32 x-16 y) = \frac{1}{8} \cdot32x - \frac{1}{8} \cdot16y$

STEP 3

Now, simplify the multiplication in each term.
$\frac{1}{6} \cdot30x =5x$ $\frac{1}{6} \cdot24y =y$ $\frac{1}{8} \cdot32x =x$ $\frac{1}{8} \cdot16y =2y$

STEP 4

Substitute these simplified terms back into the original expression.
$\frac{1}{6}(30 x-24 y)-\frac{1}{8}(32 x-16 y) =x -4y -4x +2y$

STEP 5

Combine like terms.
$5x -4x = x$ $-4y +2y = -2y$

STEP 6

Write the final simplified expression.
$x -2y$ The expression $\frac{1}{6}(30 x-24 y)-\frac{1}{8}(32 x-16 y)$ is equivalent to $x -2y$ .

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QuestionFind the equivalent expression for 16(30x−24y)−18(32x−16y)\frac{1}{6}(30 x-24 y)-\frac{1}{8}(32 x-16 y)61​(30x−24y)−81​(32x−16y).

Studdy Solution

STEP 1

Assumptions1. We are given the expression 16(30x−24y)−18(32x−16y)\frac{1}{6}(30 x-24 y)-\frac{1}{8}(32 x-16 y)61​(30x−24y)−81​(32x−16y). We need to simplify this expression to its equivalent form

STEP 2

STEP 3

Now, simplify the multiplication in each term.16⋅30x=5x\frac{1}{6} \cdot30x =5x61​⋅30x=5x16⋅24y=y\frac{1}{6} \cdot24y =y61​⋅24y=y18⋅32x=x\frac{1}{8} \cdot32x =x81​⋅32x=x18⋅16y=2y\frac{1}{8} \cdot16y =2y81​⋅16y=2y

STEP 4

Substitute these simplified terms back into the original expression.16(30x−24y)−18(32x−16y)=x−4y−4x+2y\frac{1}{6}(30 x-24 y)-\frac{1}{8}(32 x-16 y) =x -4y -4x +2y61​(30x−24y)−81​(32x−16y)=x−4y−4x+2y

STEP 5

Combine like terms.5x−4x=x5x -4x = x5x−4x=x−4y+2y=−2y-4y +2y = -2y−4y+2y=−2y

STEP 6

Write the final simplified expression.x−2yx -2yx−2yThe expression 16(30x−24y)−18(32x−16y)\frac{1}{6}(30 x-24 y)-\frac{1}{8}(32 x-16 y)61​(30x−24y)−81​(32x−16y) is equivalent to x−2yx -2yx−2y.

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QuestionFind the equivalent expression for $\frac{1}{6}(30 x-24 y)-\frac{1}{8}(32 x-16 y)$ .

Assumptions1. We are given the expression $\frac{1}{6}(30 x-24 y)-\frac{1}{8}(32 x-16 y)$ . We need to simplify this expression to its equivalent form

Now, simplify the multiplication in each term.
$\frac{1}{6} \cdot30x =5x$ $\frac{1}{6} \cdot24y =y$ $\frac{1}{8} \cdot32x =x$ $\frac{1}{8} \cdot16y =2y$

Substitute these simplified terms back into the original expression.
$\frac{1}{6}(30 x-24 y)-\frac{1}{8}(32 x-16 y) =x -4y -4x +2y$

Combine like terms.
$5x -4x = x$ $-4y +2y = -2y$

Write the final simplified expression.
$x -2y$ The expression $\frac{1}{6}(30 x-24 y)-\frac{1}{8}(32 x-16 y)$ is equivalent to $x -2y$ .