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Zorluk: ZorSolving One-Variable Linear Equations

Which of the following represents the value of pp that satisfies the given equation?

−2(4p−5)+13(15p−12)=2p−(7p−14)-2(4p - 5) + \frac{1}{3}(15p - 12) = 2p - (7p - 14)
  1. A
    -10
  2. 4Cevap
  3. C
    10
  4. D
    14

Cevap

4
The correct answer is 4. To solve the equation, first distribute the outer terms across the parentheses on both sides: −2(4p−5)-2(4p - 5) becomes −8p+10-8p + 10, 13(15p−12)\frac{1}{3}(15p - 12) becomes 5p−45p - 4, and −(7p−14)-(7p - 14) becomes −7p+14-7p + 14. Combining like terms on the left side (−8p+5p-8p + 5p and 10−410 - 4) gives −3p+6-3p + 6. On the right side, combining 2p2p and −7p-7p gives −5p+14-5p + 14. Setting these equal gives −3p+6=−5p+14-3p + 6 = -5p + 14. Adding 5p5p to both sides yields 2p+6=142p + 6 = 14, and subtracting 6 from both sides gives 2p=82p = 8. Dividing by 2 results in p=4p = 4.

Adım Adım Çözüm

1
Distribute the coefficients to remove parentheses on the left side.
−8p+10+5p−4=2p−(7p−14)-8p + 10 + 5p - 4 = 2p - (7p - 14)
Applying the distributive property is necessary to eliminate grouping symbols.
2
Distribute the negative sign to remove parentheses on the right side.
−8p+10+5p−4=2p−7p+14-8p + 10 + 5p - 4 = 2p - 7p + 14
Distributing the subtraction over the group allows all terms to be evaluated.
3
Combine like terms on each side of the equation independently.
−3p+6=−5p+14-3p + 6 = -5p + 14
Simplifying both sides makes it easier to balance the equation and isolate the variable.
4
Add 5p5p to both sides and subtract 6 from both sides.
2p=82p = 8
Performing these inverse operations groups all variable terms on one side and all constant terms on the other.
5
Divide both sides by 2.
p=4p = 4
Dividing by the coefficient isolates the variable pp, revealing its final value.

Anahtar Kavram

Solving complex multi-step linear equations using the distributive property and combining like terms.
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Konular

Solving One-Variable Linear Equations

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