Solve this equation: $-9 h-6+12 h+40=22$.
A) $h=-4 / 7$
B) $h=-4$
C) $h=24$
D) $h=4$
Answer (2)
Combine like terms: − 9 h + 12 h − 6 + 40 = 3 h + 34 .
Rewrite the equation: 3 h + 34 = 22 .
Isolate the term with h : 3 h = 22 − 34 = − 12 .
Solve for h : h = 3 − 12 = − 4 . The final answer is − 4 .
Explanation
Analyze the problem We are given the equation − 9 h − 6 + 12 h + 40 = 22 . Our goal is to solve for the variable h . Let's start by simplifying the left side of the equation by combining like terms.
Combine like terms First, combine the terms with h : − 9 h + 12 h = 3 h . Next, combine the constant terms: − 6 + 40 = 34 . So, the equation becomes 3 h + 34 = 22 .
Isolate the h term Now, we want to isolate the term with h . To do this, subtract 34 from both sides of the equation: 3 h + 34 − 34 = 22 − 34 , which simplifies to 3 h = − 12 .
Solve for h Finally, to solve for h , divide both sides of the equation by 3: 3 3 h = 3 − 12 , which gives us h = − 4 .
Examples
Solving linear equations is a fundamental skill in algebra and has many real-world applications. For example, suppose you are saving money to buy a new bicycle that costs $200. You have already saved $50, and you plan to save $15 each week. You can set up a linear equation to determine how many weeks it will take to save enough money: 50 + 15 w = 200 . Solving for w will tell you the number of weeks needed. Linear equations are also used in physics, engineering, economics, and many other fields to model and solve problems involving relationships between quantities.
The solution to the equation − 9 h − 6 + 12 h + 40 = 22 is h = − 4 , which corresponds to option B. This is found by combining like terms, isolating h , and solving for it. Thus, the answer is B) h = − 4 .
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