Solved on Jan 23, 2024

Simplify the expression $5+W-7.5W-\frac{1}{2}$ by adding or subtracting like terms.

STEP 1

Assumptions
1. We are given the expression $5 + W - 7.5 W - \frac{1}{2}$ .
2. Like terms are terms that contain the same variable raised to the same power.
3. The variable $W$ is the like term in this expression.
4. Constants (numbers without variables) are also considered like terms.

STEP 2

Identify the like terms in the expression. The like terms are the terms with the variable $W$ and the constants.

STEP 3

Combine the like terms with the variable $W$ . To do this, we add or subtract the coefficients (numerical factors) of $W$ .
$W - 7.5 W = 1W - 7.5W$

STEP 4

Subtract the coefficients of $W$ .
$1W - 7.5W = -6.5W$

STEP 5

Now, combine the constant terms $5$ and $-\frac{1}{2}$ .
$5 - \frac{1}{2}$

STEP 6

To subtract the fractions, we need a common denominator. The common denominator for $5$ and $\frac{1}{2}$ is $2$ .

STEP 7

Convert $5$ to a fraction with the common denominator $2$ .
$5 = \frac{5 \times 2}{2} = \frac{10}{2}$

STEP 8

Now, subtract the fraction $\frac{1}{2}$ from $\frac{10}{2}$ .
$\frac{10}{2} - \frac{1}{2}$

STEP 9

Subtract the numerators while keeping the common denominator.
$\frac{10}{2} - \frac{1}{2} = \frac{10 - 1}{2}$

STEP 10

Calculate the result of the subtraction.
$\frac{10 - 1}{2} = \frac{9}{2}$

STEP 11

Now, combine the result from STEP_4 and STEP_10 to get the simplified expression.
$-6.5W + \frac{9}{2}$
This is the simplified form of the original expression.

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Simplify the expression $5+W-7.5W-\frac{1}{2}$ by adding or subtracting like terms.

STEP 1

Assumptions
1. We are given the expression $5 + W - 7.5 W - \frac{1}{2}$ .
2. Like terms are terms that contain the same variable raised to the same power.
3. The variable $W$ is the like term in this expression.
4. Constants (numbers without variables) are also considered like terms.

STEP 2

Identify the like terms in the expression. The like terms are the terms with the variable $W$ and the constants.

STEP 3

Combine the like terms with the variable $W$ . To do this, we add or subtract the coefficients (numerical factors) of $W$ .
$W - 7.5 W = 1W - 7.5W$

STEP 4

Subtract the coefficients of $W$ .
$1W - 7.5W = -6.5W$

STEP 5

Now, combine the constant terms $5$ and $-\frac{1}{2}$ .
$5 - \frac{1}{2}$

STEP 6

To subtract the fractions, we need a common denominator. The common denominator for $5$ and $\frac{1}{2}$ is $2$ .

STEP 7

Convert $5$ to a fraction with the common denominator $2$ .
$5 = \frac{5 \times 2}{2} = \frac{10}{2}$

STEP 8

Now, subtract the fraction $\frac{1}{2}$ from $\frac{10}{2}$ .
$\frac{10}{2} - \frac{1}{2}$

STEP 9

Subtract the numerators while keeping the common denominator.
$\frac{10}{2} - \frac{1}{2} = \frac{10 - 1}{2}$

STEP 10

Calculate the result of the subtraction.
$\frac{10 - 1}{2} = \frac{9}{2}$

STEP 11

Now, combine the result from STEP_4 and STEP_10 to get the simplified expression.
$-6.5W + \frac{9}{2}$
This is the simplified form of the original expression.

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Simplify the expression 5+W−7.5W−125+W-7.5W-\frac{1}{2}5+W−7.5W−21​ by adding or subtracting like terms.

STEP 1

STEP 2

Identify the like terms in the expression. The like terms are the terms with the variable WWW and the constants.

STEP 3

Combine the like terms with the variable WWW. To do this, we add or subtract the coefficients (numerical factors) of WWW.W−7.5W=1W−7.5WW - 7.5 W = 1W - 7.5WW−7.5W=1W−7.5W

STEP 4

Subtract the coefficients of WWW.1W−7.5W=−6.5W1W - 7.5W = -6.5W1W−7.5W=−6.5W

STEP 5

Now, combine the constant terms 555 and −12-\frac{1}{2}−21​.5−125 - \frac{1}{2}5−21​

STEP 6

To subtract the fractions, we need a common denominator. The common denominator for 555 and 12\frac{1}{2}21​ is 222.

STEP 7

Convert 555 to a fraction with the common denominator 222.5=5×22=1025 = \frac{5 \times 2}{2} = \frac{10}{2}5=25×2​=210​

STEP 8

Now, subtract the fraction 12\frac{1}{2}21​ from 102\frac{10}{2}210​.102−12\frac{10}{2} - \frac{1}{2}210​−21​

STEP 9

Subtract the numerators while keeping the common denominator.102−12=10−12\frac{10}{2} - \frac{1}{2} = \frac{10 - 1}{2}210​−21​=210−1​

STEP 10

Calculate the result of the subtraction.10−12=92\frac{10 - 1}{2} = \frac{9}{2}210−1​=29​

STEP 11

Now, combine the result from STEP_4 and STEP_10 to get the simplified expression.−6.5W+92-6.5W + \frac{9}{2}−6.5W+29​This is the simplified form of the original expression.

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Simplify the expression $5+W-7.5W-\frac{1}{2}$ by adding or subtracting like terms.

Identify the like terms in the expression. The like terms are the terms with the variable $W$ and the constants.

Combine the like terms with the variable $W$ . To do this, we add or subtract the coefficients (numerical factors) of $W$ .
$W - 7.5 W = 1W - 7.5W$

Subtract the coefficients of $W$ .
$1W - 7.5W = -6.5W$

Now, combine the constant terms $5$ and $-\frac{1}{2}$ .
$5 - \frac{1}{2}$

To subtract the fractions, we need a common denominator. The common denominator for $5$ and $\frac{1}{2}$ is $2$ .

Convert $5$ to a fraction with the common denominator $2$ .
$5 = \frac{5 \times 2}{2} = \frac{10}{2}$

Now, subtract the fraction $\frac{1}{2}$ from $\frac{10}{2}$ .
$\frac{10}{2} - \frac{1}{2}$

Subtract the numerators while keeping the common denominator.
$\frac{10}{2} - \frac{1}{2} = \frac{10 - 1}{2}$

Calculate the result of the subtraction.
$\frac{10 - 1}{2} = \frac{9}{2}$

Now, combine the result from STEP_4 and STEP_10 to get the simplified expression.
$-6.5W + \frac{9}{2}$
This is the simplified form of the original expression.