Match each expression to its simplified form.
[tex]$(6 r+7)+(13+7 r)$[/tex] [tex]$(13-\frac{3}{2} r)-(1-r)$[/tex] [tex]$(-8-r)+(2 r-4)$[/tex]
[tex]$(7 r-\frac{3}{2})-(\frac{2}{3}+6 r)$[/tex]
[tex]$12-\frac{1}{2} r$[/tex]
[tex]$r-\frac{13}{6}$[/tex]
[tex]$13 r+20$[/tex]
[tex]$-12+r$[/tex]
Answer (2)
Simplify ( 6 r + 7 ) + ( 13 + 7 r ) to get 13 r + 20 .
Simplify ( 13 − 2 3 r ) − ( 1 − r ) to get 12 − 2 1 r .
Simplify ( − 8 − r ) + ( 2 r − 4 ) to get − 12 + r .
Simplify ( 7 r − 2 3 ) − ( 3 2 + 6 r ) to get r − 6 13 .
Match each original expression with its simplified form: ( 6 r + 7 ) + ( 13 + 7 r ) = 13 r + 20 , ( 13 − 2 3 r ) − ( 1 − r ) = 12 − 2 1 r , ( − 8 − r ) + ( 2 r − 4 ) = − 12 + r , ( 7 r − 2 3 ) − ( 3 2 + 6 r ) = r − 6 13
Explanation
Analyzing the Problem We need to simplify each of the given expressions and match them with their corresponding simplified forms. Let's start with the first expression.
Simplifying the First Expression The first expression is ( 6 r + 7 ) + ( 13 + 7 r ) . We combine the like terms, which are the terms with r and the constant terms. So we have 6 r + 7 r + 7 + 13 . This simplifies to 13 r + 20 .
Simplifying the Second Expression The second expression is ( 13 − 2 3 r ) − ( 1 − r ) . We distribute the negative sign to both terms inside the second parenthesis: 13 − 2 3 r − 1 + r . Combining like terms, we have 13 − 1 − 2 3 r + r . This simplifies to 12 − 2 1 r .
Simplifying the Third Expression The third expression is ( − 8 − r ) + ( 2 r − 4 ) . We combine the like terms: − 8 − r + 2 r − 4 . This simplifies to − 12 + r .
Simplifying the Fourth Expression The fourth expression is ( 7 r − 2 3 ) − ( 3 2 + 6 r ) . We distribute the negative sign: 7 r − 2 3 − 3 2 − 6 r . Combining like terms, we have 7 r − 6 r − 2 3 − 3 2 . This simplifies to r − 6 9 − 6 4 = r − 6 13 .
Matching Expressions Now we match each original expression with its simplified form:
( 6 r + 7 ) + ( 13 + 7 r ) simplifies to 13 r + 20 .
( 13 − 2 3 r ) − ( 1 − r ) simplifies to 12 − 2 1 r .
( − 8 − r ) + ( 2 r − 4 ) simplifies to − 12 + r .
( 7 r − 2 3 ) − ( 3 2 + 6 r ) simplifies to r − 6 13 .
Examples
Simplifying expressions is a fundamental skill in algebra and is used in many real-world applications. For example, when calculating the total cost of items with discounts or taxes, you need to combine like terms to simplify the expression and find the final cost. Also, in physics, when analyzing forces or motion, you often need to simplify algebraic expressions to solve for unknown variables.
Each expression was simplified step-by-step, leading to matches of the original expressions to their simplified forms: (6r + 7) + (13 + 7r) = 13r + 20, (13 - 3/2r) - (1 - r) = 12 - 1/2r, (-8 - r) + (2r - 4) = -12 + r, and (7r - 3/2) - (2/3 + 6r) = r - 13/6.
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