$5(t+7)-6=59$

Part 1 of 2

Is the equation a conditional equation, a contradiction, or an identity?

Part 2 of 2

What is the solution set?

The equation 5 ( t + 7 ) − 6 = 59 is categorized as a conditional equation because it has a specific solution, which is t = 6 . The solution set for this equation is oxed{\{6\}} .
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Answered by Anonymous | 2025-07-04

Distribute and simplify the equation: 5 t + 35 − 6 = 59 becomes 5 t + 29 = 59 .
Isolate the variable by subtracting 29 from both sides: 5 t = 30 .
Solve for t by dividing both sides by 5: t = 6 .
The equation is conditional, and the solution set is 6 ​ .

Explanation

Understanding the Problem We are given the equation 5 ( t + 7 ) − 6 = 59 . Our goal is to classify this equation as either a conditional equation, a contradiction, or an identity, and then to find its solution set.

Simplifying the Equation First, we simplify the equation by distributing the 5 and combining like terms: 5 ( t + 7 ) − 6 = 59
5 t + 35 − 6 = 59
5 t + 29 = 59

Isolating the Variable Next, we isolate t by subtracting 29 from both sides of the equation: 5 t + 29 − 29 = 59 − 29 5 t = 30

Solving for t Now, we solve for t by dividing both sides by 5 :
5 5 t ​ = 5 30 ​ t = 6

Classifying the Equation and Finding the Solution Set Since the equation is true for only one specific value of t (namely, t = 6 ), it is a conditional equation. The solution set is the set containing only the number 6 .


Examples
Conditional equations are useful in many real-world scenarios. For example, suppose you want to save up for a new bicycle that costs $200. You already have $50 saved, and you plan to save $10 each week. The equation 50 + 10 w = 200 is a conditional equation that represents this situation, where w is the number of weeks. Solving for w will tell you exactly how many weeks it will take to save enough money to buy the bicycle. In this case, w = 15 , so it will take 15 weeks to save enough money.

Answered by GinnyAnswer | 2025-07-04